Permutations and Combinations

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Evaluate (i) 8! (ii) 4! - 3!

Is 3! + 4! = 7!?

Compute 8!/(6! × 2!)

If 1/6! + 1/7! = x/8!, find x

Evaluate n!/(n-r)!, when (i) n = 6, r = 2 (ii) n = 9, r = 5.

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

How many 4-digit numbers are there with no digit repeated?

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

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 can not hold more than one position?

Find n if n-1P₃ : nP₄ = 1 : 9.

Find r if (i) ⁵Pᵣ = 2⁶Pᵣ₋₁ (ii) ⁵Pᵣ = ⁶Pᵣ₋₁.

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

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if (i) 4 letters are used at a time, (ii) all letters are used at a time, (iii) all letters are used but first letter is a vowel?