Test Session Chapter 7 Permutation and Combination (1st Year Mathematics)

Multiple Choice Questions (MCQs)

Short Answer Questions

Permutation & Combination Formulas

Factorial:

n! = n × (n-1) × … × 2 × 1

0! = 1

Permutation (Arrangement):

^nP_r = \frac{n!}{(n-r)!}

Order matters

Combination (Selection):

^nC_r = \frac{n!}{r!(n-r)!}

Order doesn’t matter

Circular Permutation:

n distinct objects: (n-1)!

If clockwise/anticlockwise same: (n-1)!/2

Subsets:

Set with n elements has 2ⁿ subsets

Including empty set and itself

Permutation with Repetition:

nⁿ for n objects taken n at a time

With restrictions: divide by factorial of repeated items

Permutation Calculator (ⁿPᵣ)

Value of n:

Value of r:

Combination Calculator (ⁿCᵣ)

Value of n:

Value of r:

Detailed Answer Questions

Question 1 (5 marks)

There are four distinct coloured balls and four boxes of same colours as those of the balls. Determine the number of possible ways the balls, one each in a box, can be placed such that a ball does not go to a box of its own colour?

Question 2 (5 marks)

A box contains 15 cards from (1 – 15). Danish is to select 5 cards. If all the selected cards are the first five multiples of 2, then Danish will win the game. Find Danish’s chance of winning the game, when: (i) Order is important (ii) Order is not important. (Example 13)

Question 3 (5 marks)

A photographer needs to arrange 7 models for a photo shoot. There are 4 male models and 3 female models. (a) How many different arrangements are possible if there are no restrictions. (b) How arrangements are possible if the male models must stand together and the female models must stand together? (c) How many arrangements are possible if the male and female models must alternate?

Note: Answer any 2 questions. Each question carries 5 marks.

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