Permutations and Combinations Quiz Set 014

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.

The first has 6 options, the second also has 6 options, and so on. This is expressed as 6 × 6 × 6 × 6, which evaluates to 1296.

This word has 10 different letters. The number of possibilities is ¹⁰P₄ = 5040.

The required count is ⁴C₂ × ⁹C₂ = 216.

The secretary can be any of the 13 members, the general-secretary can then be any of the (13 - 1) members. So the answer is 13 × (13 - 1) = 156.