Question

1. In the problems below, A and B can be repeated.
   (a) How many 10 letter words can be formed using the letters A and B? (b) How many of these 10 letter words contain at most 2 A’s?

Answer 1

a) since A and B can be repeated.

The first latter of the 10 letter word is either A or B, so there have 2 choice.

Similarly for 2nd , 3rd ... 10th positions there have 2 choice.

Therefore total number of 10 letter word, fomed using the letters A and B, is (10 times), i.e, , i.e, 1024.

b) at most 2 A's means either there have no A or one A or 2 A's.

Number of words , among these 10 letter words, which doesn't contain A is .

Number of words, among these 10 letter words, which contains only 1 A is .

Number of words, among these 10 letter words, which contains 2 A is .

Therefore number of words, among these 10 letter words, contains at most 2 A's is



= 1+10+45

= 56