Question

10) No many distinct arrangerients of the letters in the word Mississippi are possible? 10,016,800 B) 34650 C) 1152 D) 7920 11) From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. 11)

Answer 1

(10) M I S S I S S I P P I contains a total of 11 letters, where I is repeated 4 times, S 4 times and P 2 times.

The rule states that for an n letter word, where a letter of 1 type occurs x times, another letter occurs y times and so on, then the total number of words = n!/ (x1 * y! ....)

Therefore number of words possible with MISSISSIPPI = 11! / (4!*4!*2!) = 39916800 / (24 * 24 * 2) = 34,650 (Option B)

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(11) Total possible ways of getting a committee of 5 from 9 names = 9C5 = 9! / [(9 - 4)! * 4!] = 9 * 8 * 7 * 6 / (4 * 3 * 2 * 1) = 126

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