From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

14

How many even numbers of three digits each can be made with the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

15

Find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated. How many of these will be even?

17

Find n if ^n-1P₃ : ⁿP₄ = 1: 9.

18

Find r if :  (i) 5P_r = 2 6P_r-1   (ii) 5P_r = 6P_r-1