Find n if ^n-1P₃ : ⁿP₃ = 1 : 9.

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?

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?

Find r if (i)⁵P_r : 2⁶P_r-1 (ii) ⁵P_r : ⁶P_r-1

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?