In how many ways can a team of 5 Batsman and 5 Bowler be selected out of a total of 10 Batsman and 10 Bowler?
In how many ways can a team of 5 Batsman and 5 Bowler be selected out of a total of 10 Batsman and 10 Bowler? Correct Answer 63504
Given:
Total number of Batsman = 10
Total number of Batsman to be selected = 5
Total number of Bowler = 10
Number of Bowler to be selected = 5
Concept used:
nCr = n!/
Where,
r = Men selected from total
n = Total men
Calculation:
The Number of ways in which 5 Batsman can be selected from 10 Batsman = 10C5
⇒ 10!/
⇒ 10!/(5! × 5!)
⇒ (10 × 9 × 8 × 7 × 6 × 5!)/(5 × 4 × 3 × 2 × 1 × 5!)
⇒ (10 × 9 × 8 × 7 × 6)/(5 × 4 × 3 × 2 × 1) = 252
The Number of ways in which 5 Bowler can be selected from 10 Bowler = 10C5
⇒ 10!/
⇒ 10!/(5! × 5!)
⇒ (10 × 9 × 8 × 7 × 6 × 5!)/(5 × 4 × 3 × 2 × 1 × 5!)
⇒ (10 × 9 × 8 × 7 × 6)/(5 × 4 × 3 × 2 × 1) = 252
The Number of ways in which 5 Batsman and 5 Bowler can be chosen = 10C5 × 10C5
⇒ 252 × 252 = 63504
∴ The number of ways in which 5 Batsman and 5 Bowler can be chosen is 63504
