Question 1

[Exercise 7.1] Evaluate: (i) 5!, (ii) 7!/5!, (iii) 6P2, (iv) 6C2.

Accepted Answer

(i) 5! = 120(ii) 7!/5! = (7 × 6 × 5!)/5! = 42(iii) 6P2 = 6!/(6-2)! = 6!/4! = 30(iv) 6C2 = 6!/(2! × 4!) = (6 × 5)/2 = 15

Question 2

[Exercise 7.1] How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition?

Accepted Answer

Number of arrangements of 6 digits taken 3 at a time:6P3 = 6 × 5 × 4 = 120120 distinct 3-digit numbers.

Question 3

[Exercise 7.1] In how many ways can the letters of the word 'MONDAY' be arranged, keeping the vowels together?

Accepted Answer

MONDAY has vowels O and A.Treat (OA) as one unit. Units: (OA), M, N, D, Y = 5 units.Arrangements = 5! = 120.O and A can swap internally in 2! = 2 ways.Total = 120 × 2 = 240 ways.

Question 4

[Exercise 7.1] A committee of 3 is to be chosen from 8 students. In how many ways can this be done?

Accepted Answer

Combinations (order does not matter):8C3 = 8!/(3! × 5!) = (8 × 7 × 6)/(3 × 2 × 1) = 56 ways

Question 5

[Exercise 7.1] How many numbers greater than 1000 but less than 4000 can be formed with the digits 0, 1, 2, 3, 4 if repetition of digits is allowed?

Accepted Answer

4-digit numbers between 1000 and 4000.Thousands digit: 1, 2, or 3 (3 choices).Hundreds, tens, units: each 5 choices (0,1,2,3,4).Total = 3 × 5 × 5 × 5 = 375 numbers

Permutations and Combinations - Important Questions