Permutations & Combinations
Team selection with constraints
nta_pyq_2025_apr
Grade 12
Question:
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and$vice-captain$respectively of the team should be included. Then the total number of ways such a selection can be made, is
Step-by-Step Solution
Key Concept: Choose batsmen and bowlers with the minimum batsmen condition by summing valid cases.
7 Batsmen \& 6 Bowlers$(2)$To select 10 players including atleast 4 Batsmen \& 4 Bowlers Captain \&$vice-captain$already selected 6 5 6 5 6 5 No. of$ways = C_{5}$$\times$$C_{3} + C_{4}$$\times$$C_{4} + C_{3}$$\times$$C_{5} = 6$$\times$$10 + 15$$\times$$5 + 20$$\times$$1 = 60 + 75 + 20 = 155$
Correct Answer: 2