1 Amale and a female typist are needed in an institution If 10 ladies and 15 gents apply - Maths - Permutations and Combinations

Question

1 Amale and a female typist are needed in an institution If 10
ladies and 15 gents apply then in hw many ways can the selection be
made, given one particular pair does not wish to be together

Lalit Mehra · Accepted Answer

Number of ladies = 10

Number of gents = 15

Given, a particular pair do not wish to be together. Therefore, we consider two cases for the selection.

Case 1: If a particular man is not chosen, then number of ways of selection = $^{10} C_{1} \times^{14} C_{1} = 10 \times 14 = 140$

Case 2: If a particular woman is not chosen, then number of ways of selection = $^{9} C_{1} \times^{15} C_{1} = 9 \times 15 = 135$

By addition principle of counting,

Total number of ways of selection = 140 + 135 = 275

1. Amale and a female typist are needed in an institution. If 10 ladies and 15 gents apply then in hw many ways can the selection be made, given one particular pair does not wish to be together