Question

There are 5 different Hindi books, 6 different Urdu books and 8 different Sanskrit books. In how many ways can a pair of books be selected if the selected books are from different languages ?

Answer 1

number of Hindi books = 5
number of Urdu books = 6
number of Sanskrit books = 8
Total number of books = 19
The possible sets of 2 languages are Hindi and Urdu , Hindi and Sanskrit , Sanskrit and Urdu.
number of ways of selecting 2 books each from Hindi and Urdu is $5_{C _{1} }$ × $6_{C _{1} }$ = 5 × 6 = 30
number of ways of selecting 2 books each from Hindi and Sanskrit is $5_{C _{1} }$ × $8_{C _{1} }$ = 5 × 8 = 40
number of ways of selecting 2 books each from Sanskrit and Urdu is $5_{C _{1} }$ × $6_{C _{1} }$ = 8 × 6 = 48
total number of ways of selection of 2 books from a whole of 19 is 30 + 40 + 48 = 118.