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

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