Question

A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?

Answer 1

Answer: 420 different codes are possible.

Explanation:

The number of possible codes can be given by

N = n!/(ra! × rb! × rc! × rd!)

Where;

n is the total number of letters in the code.

ra,rb,rc and rd are number of occurrence of A,B,C and D respectively

Given: n= 7, ra=3, rb=2, rc=1, rd=1.

Substituting the values, we have.

N = 7!/(3!×2!×1!×1!)

N = 5040/12

N= 420