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19 July, 13:31

How many four-letter code words are possible using the letters in IOWA if (a) The letters may not be repeated? (b) The letters may be repeated

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  1. 19 July, 14:54
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    a. 24ways

    b. 256ways

    Step-by-step explanation:

    the letters IOWA contains for letters, since we are to arrange without repeating any letter, we permutate the letters.

    For permutation of n object in r ways is expressed as

    P (n, r) = n! / (n-r) !

    hence for n=4 and r=4, we have P (4,4) = 4! / (4-4) !

    P (4,4) = 4! / (0) !

    P (4,4) = 4*3*2*1=24ways

    b. To arrange the letters such that each letter can be repeated, we can arrange the letter I in four ways, letter O can be arrange in four ways, letter W can be arranged in four ways and letter A can be arranged in four ways ...

    Hence we arrive at

    4*4*4*4=256ways
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