Revision on Logic and Combinatorics

Find the number of ways of selecting 2 vowels and 2 consonants from the letters of the set {I, N, T, E, R, V, A, L}.

• 30

• 10

• 13

• 70

How many 4 card hands that contain exactly 3 aces and 1 queen can be chosen from a 52 card deck?

• 4

• 16

• 8

• 270725

How many different 2 digit numbers can be formed using {2, 3, 4, 5, 6, 7, 8}, if repetition of a digit is not allowed?

• 79

• 64

• 56

• 42

How many 4 digit number secret codes can be formed for the credit card of a bank using the digits {1, 2, 3, 4, 5, 6, 7, 8, 9}? (Repetition of a digit is allowed.)

• 4⁹

• 4×9

• 9⁴

• 9×8×7×6

How many 2-letter words can be made using the English alphabet (consisting of 26 letters), if repetition of a letter is not allowed?

• 26!

• 26²

• 2!

• 26×25

How many different teams of 8 can be chosen from 12 players?

• ₁₂C₈ = 495

• 12×8 = 96

• 12⁸

• 8¹²

There are 7 pens and 10 pencils in a box. How many ways can 4 pens be chosen from the box?

• ₁₀C₄ = 210

• ₇C₄ = 35

• ₁₇C₄ = 2380

• 4!

In a group of 20 members, 12 are boys and 8 are girls. Find the number of ways of forming a 15 member committee which should include exactly 9 boys.

• 15504

• 167960

• 220

• 6160

How many permutations of the letters are there in the word GORGEOUS?

• 40320

• 10080

• 20160

• 1680

In an examination paper there are 12 multiple choice questions, each has 4 choices. Find the number of ways of answering these 12 questions.

• 12⁴ = 20736

• 12 × 4 = 48

• 4¹² = 16777216

• ₁₂C₄ = 495