In the word "gallipolis"
there are 10 letters (n =
10).
"l" appears 3 times (n1 =
3).
"i" appears 2 times (n2 =
2).
And 5 letters appear once (n3 =1, n4 =
1, n5 =1, n6 =1, n7 =1)
The number of permutations that can be made with these 10 letters is;
P =
n!/(n1!n2!n3!n4!n5!n6!n7!) =
10!/(3!∙2!∙1!∙1!∙1!∙1!∙1!) =
302 400
act
2520
There are 7893600 permutations.
First of all, find the total number of not-necessarily distinguishable permutations. There are 12 letters in hippopotamus, so use 12! (12 factorial), which is equal to 12 x 11x 10 x9 x8 x7 x6 x5 x4 x3 x2 x1. 12! = 479001600.Then count the of each letter and calculate how many permutations of each letter can be made. For example, here is 1 h, so there is 1 permutation of 1 h.H 1I 1P 60 2T 1A 1M 1U 1S 1Multiply these numbers together. 1 x1 x6 x2 x1 x1 x1 x1 x1 = 12Divide 12! by this number. 479001600 / 12 = 39,916,800 Distinguishable Permutations.
There are 9 * 8 * 7, or 504, three letter permutations that can be made from the letters in the work CLIPBOARD.
There are 12 letters in the following, with two pairs of doubles so the answer is 12!/[2!*2!] = 119,750,400
The only five letter word that can be made with those letters is 'ditto'.Other words that can be made with the letters in 'ditto' are:dodotIidittotot
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
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 5,273,912,160 permutations of 5 numbers out of 90.
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.