the number of permutations in part a

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a.) How many Permutations are there for the nine letters a, b, c, d, e, f, g, i, j ?b.) Considering the number of permutations in part a. How many start with the letterc) Considering the number of permutations in part a. How many start with the letter a and end with the letter i?
There is a group of 12 diplomats sitting around a circular table with 12 seats. Of the 12 diplomats there are 7 women and 5 men. How many ways can the seats be assigned so that no two men are seated next to each other?
In how many ways can 16 books be distributed among 4 children so that a) each child gets 4 books?b) the see oldest children get 6 books each and the two youngest get 2 books each?
Determine the coefficient of a.) xyg„A3 in (x+y+z)^5 b.)
Two n-digit integers (leading zeros allowed) are considered equivalent if one is a rearrangement of the other. So that for example 000123, 123000, 102030 are all considered to be equivalent 6 digit integers.a.) How many 6 digit integers are not equivalent?b.) If the digits 4,5 can appear at most once, how many non-equivalent 6 digit integers are there?

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