How many permutations can be made of the letters of the following word "proposition" when taken all at a time?
a) 11! /24
b) 11! /12 1
c) 1! /6

11!/24 permutations can be made of the letters of the following word "PROPOSITION" when taken all at a time by using the permutation formula. This problem can be solved using the permutation formula (Total number of the alphabet)!/(repetition of P letter)!(repetition of O letter)!(repetition of I letter)! resulting in 11!/2!*3!*2! = 11!/24. Permutation is a term used for describing the method for arranging all members of some set into some sequence or order and in this problem, letter P, letter R, letter O, letter S, letter I, and letter N are the members of the set and the combination of these letters is the sequence or order.