The number of ways in which any four letters can be selected from the word "EXAMINATION” is ______.
The number of ways in which any four letters can be selected from the word "EXAMINATION” is ______.
The correct option is B 136
Word "EXAMINATION" has 11 letters out of them there are 3 pairs: {A, A}, {l, l} and {N, N}.
So, number of distinct letters is 8
Four letters can be selected in the following ways
Case (i) all different letters out of 8 letters.
The number of ways is 8C4 = 70
Case (ii) two letters are alike and other two are distinct
The number of ways is 3C1× 7C2 = 63
3C1 is a number of ways to choose which two letters will be alike from 3 pairs and 7C2 is
number of ways to choose other two distinct letters from 7 letters which are left
Case (iii) two letters are alike and other two letters are also alike
The number of ways is 3C2 = 3
3C2 is a number of ways of choosing two pairs of alike letter from 3 such pairs
Therefore, required number of ways =70+63+3=136
136
Word "EXAMINATION" has 11 letters out of them there are 3 pairs: {A, A}, {l, l} and {N, N}.
So, number of distinct letters is 8
Four letters can be selected in the following ways
Case (i) all different letters out of 8 letters.
The number of ways is 8C4 = 70
Case (ii) two letters are alike and other two are distinct
The number of ways is 3C1× 7C2 = 63
3C1 is a number of ways to choose which two letters will be alike from 3 pairs and 7C2 is
number of ways to choose other two distinct letters from 7 letters which are left
Case (iii) two letters are alike and other two letters are also alike
The number of ways is 3C2 = 3
3C2 is a number of ways of choosing two pairs of alike letter from 3 such pairs
Therefore, required number of ways =70+63+3=136
