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

it is probably the graph on the bottom right.