240
To select a committee of 3 people from 10, you can use the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ). Here, ( n = 10 ) and ( k = 3 ). This gives ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, there are 120 ways to select a committee of 3 people from 10.
To select 3 marbles from a jar containing 10 different colored marbles, you can use the combination formula ( C(n, r) = \frac{n!}{r!(n-r)!} ). Here, ( n = 10 ) and ( r = 3 ). Thus, the number of ways to select the marbles is ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, there are 120 different ways to select 3 marbles.
If he must answer the last question, he effectively needs to select 6 from 10. This can be done in 10C6 = 10*9*8*7/(4*3*2*1) = 210 ways.
If he must include the last question, then his choices really boil down tohow many ways he can select 4 more from the remaining 11.The number of ways he can select 4 from 11 is (11 x 10 x 9 x 8) = 7,920 ways .But each group of 4 can be selected in 24 different ways.So he can only wind up with 7920/24 = 330 different groups of questions.
To assign 10 positions from 13 players, you can use the concept of permutations since the order of selection matters. The number of ways to select and arrange 10 players out of 13 is given by the permutation formula ( P(n, r) = \frac{n!}{(n-r)!} ). For this scenario, it would be ( P(13, 10) = \frac{13!}{(13-10)!} = \frac{13!}{3!} ), resulting in 13,860 different ways to assign the positions.
To select a committee of 3 people from 10, you can use the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ). Here, ( n = 10 ) and ( k = 3 ). This gives ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, there are 120 ways to select a committee of 3 people from 10.
Aquiel can select 4 books out of 10 best sellers, which can be done in 10 choose 4 ways, also denoted as "10C4" or "10 choose 4". This would result in 210 different ways for Aquiel to select and read the 4 books.
they can complete this exam 300 ways
To select 3 marbles from a jar containing 10 different colored marbles, you can use the combination formula ( C(n, r) = \frac{n!}{r!(n-r)!} ). Here, ( n = 10 ) and ( r = 3 ). Thus, the number of ways to select the marbles is ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, there are 120 different ways to select 3 marbles.
If he must answer the last question, he effectively needs to select 6 from 10. This can be done in 10C6 = 10*9*8*7/(4*3*2*1) = 210 ways.
I'm going with 25,200 3 men out of 10 may be chosen in 10C3 ways = 10 ! / 3! 7 ! = 120 ways. 4 women may be chosen out of 10 in 10C4 = 10 ! / 4! 6! ways = 210 ways. Therefore, a committee with 3 men and 4 women can be formed in 120 x 210 = 25,200 ways.
If he must include the last question, then his choices really boil down tohow many ways he can select 4 more from the remaining 11.The number of ways he can select 4 from 11 is (11 x 10 x 9 x 8) = 7,920 ways .But each group of 4 can be selected in 24 different ways.So he can only wind up with 7920/24 = 330 different groups of questions.
Oh, what a delightful question! To find the total ways a dinner patron can select 3 appetizers out of 6, we use combinations, which is like a recipe for choosing items without regard to the order. So, the dinner patron can choose 3 appetizers out of 6 in 20 ways. Similarly, they can choose 2 vegetables out of 5 in 10 ways. So, the total ways to select 3 appetizers and 2 vegetables is 20 * 10 = 200 ways. Isn't that just lovely?
10 ways.10 ways.10 ways.10 ways.
The answer depends on how many numbers you select!The answer depends on how many numbers you select!The answer depends on how many numbers you select!The answer depends on how many numbers you select!
To assign 10 positions from 13 players, you can use the concept of permutations since the order of selection matters. The number of ways to select and arrange 10 players out of 13 is given by the permutation formula ( P(n, r) = \frac{n!}{(n-r)!} ). For this scenario, it would be ( P(13, 10) = \frac{13!}{(13-10)!} = \frac{13!}{3!} ), resulting in 13,860 different ways to assign the positions.
The number of ways is 10C5 = 10!/(5!*5!) = 10*9*8*7*6/(5*4*3*2*1) = 252