For first course there are 10 choices
for second 9
for third 8
for fourth 7
total choices of selecting = 10*9*8*7=5040
10! permutations of the word "Arithmetic" may be made.
There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
5*4*3*2*1 = 120
"Permutations" do consider the order. If you want the order ignored, then you're looking for "combinations". 3-digit permutations, repetition allowed: 9 x 9 x 9 = 729 3-digit permutations, no repetition: 9 x 8 x 7 = 504 3-digit combinations, no repetition = 504/6 = 84.
If it alternates and you start with a letter, then there are 11,232,000 permutations. Then if you start with a number and alternate, there are another 11,232,000 permutations, for a total of 22,464,000 permutations. If you exclude the letters I, S, B, and O (because they look kind-of like 1, 5, 8, & 0 - kind-of important on license plates) then you are down to 6,652,800 & 13,305,600 respectively.
10! permutations of the word "Arithmetic" may be made.
There are 7893600 permutations.
There are 5,273,912,160 permutations of 5 numbers out of 90.
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There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
2520
There are courses you can take in college for this career, but there are also individual organizations and outside classes that are made specifically for this career path. These organizations consist or programs and training.
5*4*3*2*1 = 120
"Permutations" do consider the order. If you want the order ignored, then you're looking for "combinations". 3-digit permutations, repetition allowed: 9 x 9 x 9 = 729 3-digit permutations, no repetition: 9 x 8 x 7 = 504 3-digit combinations, no repetition = 504/6 = 84.
Assuming you mean permutations of three digits, then the set of numbers that can be made with these digits is: 345 354 435 453 534 543 There are six possible permutations of three numbers.
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The question can be re-stated as asking for the total number of permutations that can be derived from the following two groups of digits: AAABCD and AABBCD, where A, B, C and D are different. The number of ways of choosing the digit A, to be used three times, out of the ten digits {0, 1, 2, ... 9} is 10. Having done that, the number of ways of selecting 3 from the remaining 9 digits is 9C3 = (9*8*7)/(3*2*1) = 84. Thus there are 10*84 = 840 combinations of the form AAABCD. You now need all the distinct permutations of these 6 digits. The total number of permutations of 6 digits is 6! but because 3 of the digits are the same, these permutations are not all distinct. In fact, there are 6!/3! = 120 distinct permutations. That makes a total of 840*120 = 100800 such numbers. Next, the number of ways of choosing the digits A and B, each to be used twice, out of the ten digits {0, 1, 2, ... 9} is 10C2 = (10*9)/(2*1) = 45. Having done that, the number of ways of selecting C and D from the remaining 8 digits is 8C2 = (8*7)/(2*1) = 28. Thus there are 45*28 = 1260 combinations of the form AAABCD. You now need all the distinct permutations of these 6 digits. The total number of permutations of 6 digits is 6! but because 2 pairs of these digits are the same, these permutations are not all distinct. In fact, there are 6!/(2!*2!) = 180 distinct permutations. That makes a total of 1260*180 = 226800 such numbers. The grand total is, therefore, 100800 + 226800 = 327600 6-digit numbers made from 4 distinct digits.