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What is the number of distinct arrangements of the letters of the word UGCCSIR so that U and you cannot come together?
To find the number of distinct arrangements of the letters in "UGCCSIR" where U and C do not come together, first calculate the total arrangements of the letters without restrictions. The word has 7 letters with the letter C repeated twice, so the total arrangements are ( \frac{7!}{2!} = 2520 ).
Next, calculate the arrangements where U and C are together by treating "UC" as a single entity. This gives us the letters "UC, G, C, S, I, R", which can be arranged in ( \frac{6!}{2!} = 360 ) ways (since C is still repeated).
Finally, subtract the arrangements where U and C are together from the total arrangements: ( 2520 - 360 = 2160 ). Thus, there are 2160 distinct arrangements where U and C do not come together.
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How many different arrangements of the letters in the word SMILE are there?
The word "SMILE" consists of 5 distinct letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 5!. Therefore, the total number of arrangements is 5! = 120.
How many distinct ordered arrangements can be made with the letters of mississippi?
There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.
How many distinct arrangements can be made from the word college?
The word "college" has 7 letters, including 2 'l's and 2 'g's, which are repeated. To find the number of distinct arrangements, we use the formula for permutations of multiset: [ \frac{n!}{n_1! \cdot n_2!} ] where (n) is the total number of letters, and (n_1), (n_2) are the frequencies of the repeated letters. Here, (n = 7), (n_1 = 2) (for 'l'), and (n_2 = 2) (for 'g'): [ \text{Distinct arrangements} = \frac{7!}{2! \cdot 2!} = \frac{5040}{4} = 1260. ] Thus, there are 1,260 distinct arrangements of the letters in "college."
How many arrangements of the letters BOX are possible if you use each letter only once in each arrangement?
The word "BOX" consists of 3 distinct letters. The number of arrangements of these letters can be calculated using the factorial of the number of letters, which is 3! (3 factorial). Therefore, the total number of arrangements is 3! = 3 × 2 × 1 = 6. Thus, there are 6 possible arrangements of the letters in "BOX."
What is the no of linear arrangements of the four letters in CALL is?
To find the number of linear arrangements of the letters in "CALL," we need to consider the repetitions of letters. The word "CALL" has 4 letters where 'L' appears twice. The formula for arrangements of letters with repetitions is given by ( \frac{n!}{p1! \times p2! \times \ldots} ), where ( n ) is the total number of letters and ( p1, p2, \ldots ) are the frequencies of each repeated letter. Therefore, the number of arrangements is ( \frac{4!}{2!} = \frac{24}{2} = 12 ). Thus, there are 12 distinct arrangements of the letters in "CALL."
What is the number of distinct arrangements of the letters of the word ugccsir so that you and i cannot come together?
from itertools import permutationsfrom string import joinarrangements = [ ]for p in permutations ( 'ugccsir', 6 ) :arrangement = join ( p, '' )if 'ui' in arrangement :continueif not arrangement in arrangements :arrangements . append ( arrangement )print len ( arrangements )The above Python code gives a result of 2,220.
How many distinct arrangements can be made with the letters in the word banana?
There are 6!/(3!*2!) = 60 arrangements.
How many different arrangements of the letters in the word SMILE are there?
The word "SMILE" consists of 5 distinct letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 5!. Therefore, the total number of arrangements is 5! = 120.
How many distinct arrangements can be made with the letters in the word BOXING?
The number of distinct arrangements of the letters of the word BOXING is the same as the number of permutations of 6 things taken 6 at a time. This is 6 factorial, which is 720. Since there are no duplicated letters in the word, there is no need to divide by any factor.
How many distinct arrangements can be made with the letters in the word surprising?
Take note of the word "surprising":There are 10 letters total.There are 2 r's.There are 2 i'sThere are 2 s's.There are 10! total ways to arrange the letters. Since repetition is not allowed for the arrangements, we need to divide the total number of arrangements by 2!2!2! Therefore, you should get 10!/(2!2!2!) distinct arrangements
How many distinct ordered arrangements can be made with the letters of mississippi?
There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.
How many distinct arrangements can be made from the word college?
The word "college" has 7 letters, including 2 'l's and 2 'g's, which are repeated. To find the number of distinct arrangements, we use the formula for permutations of multiset: [ \frac{n!}{n_1! \cdot n_2!} ] where (n) is the total number of letters, and (n_1), (n_2) are the frequencies of the repeated letters. Here, (n = 7), (n_1 = 2) (for 'l'), and (n_2 = 2) (for 'g'): [ \text{Distinct arrangements} = \frac{7!}{2! \cdot 2!} = \frac{5040}{4} = 1260. ] Thus, there are 1,260 distinct arrangements of the letters in "college."
How many arrangements of the letters BOX are possible if you use each letter only once in each arrangement?
The word "BOX" consists of 3 distinct letters. The number of arrangements of these letters can be calculated using the factorial of the number of letters, which is 3! (3 factorial). Therefore, the total number of arrangements is 3! = 3 × 2 × 1 = 6. Thus, there are 6 possible arrangements of the letters in "BOX."
What is the no of linear arrangements of the four letters in CALL is?
To find the number of linear arrangements of the letters in "CALL," we need to consider the repetitions of letters. The word "CALL" has 4 letters where 'L' appears twice. The formula for arrangements of letters with repetitions is given by ( \frac{n!}{p1! \times p2! \times \ldots} ), where ( n ) is the total number of letters and ( p1, p2, \ldots ) are the frequencies of each repeated letter. Therefore, the number of arrangements is ( \frac{4!}{2!} = \frac{24}{2} = 12 ). Thus, there are 12 distinct arrangements of the letters in "CALL."
How many words can be formed from the letters of the word IMAGINARY so that the vowels never come together?
The word "IMAGINARY" has 9 letters, including 4 vowels (I, A, I, A) and 5 consonants (M, G, N, R, Y). To find the number of arrangements where the vowels do not come together, first calculate the total arrangements of the letters (considering the repeated vowels) and then subtract the arrangements where the vowels are together, treating them as a single unit. After performing these calculations, the total number of arrangements where the vowels never come together is found to be 2880.
How many arrangements can be made with the letters spineless?
The word "spineless" has 9 letters, including 3 s's and 2 e's, so the number of distinct permutations of the letters is: 9!/(3!2!) = 30,240
How many distinct three letter arrangements can be found from the letters in mathematics?
The number of different three letter arrangements that can be done from theletters in the word "mathematics"is; 11P3 =11!/(11-3)! =990
