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

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 =

Case 2: If a particular woman is **not **chosen, then number of ways of selection =

By addition principle of counting,

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

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