Kenneth H Rosen 7th edition

Question

Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.

Answer 1

Suppose you want to dress and you have 3 pants 2 shirts. So for first shirt there are 3 pants and for another one another 3. So total there are 6 different styles in which you can dress.

Now similarly, let us take only 3 for loop of i, j and m. For the first for loop i let it iterate from 1 to 3, for j 1 to 3 and m 1 to 2.

For first i = 1 , j can take 3 values and for each 3 values of j, m will take 2 iteration.

So k will increment twice k=2 after first iteration of j.

At last iteration of j of i=1.

K will be twice * no of iterations of j

So k= 6

Now i =2

Again k which increment its value from 6 to 12.

At last i=3, k will be again 12+6.

So at the end k will be 18.

i.e. k = 3*3*2.

Which is same as k = n1*n2*n3.

n1- range of i.

n2- range of j.

n3- range of k.

This is same as the number of ways for dressing if you have n1 pants, n2 shirts and n3 shoes.

Apply the product rule.