At Least 4 Batsmen & 4 Bowlers? Count Selections FAST ⚡
❓ Question From a group of 7 batsmen and 6 bowlers , 10 players are to be chosen for a team, which should include: ✔ at least 4 batsmen ✔ at least 4 bowlers ✔ and MUST include one batsman (captain) and one bowler (vice-captain) Find the total number of ways such a team can be selected. 🖼️ Question Image ✍️ Short Solution This is a classic combinations + constraints problem. 👉 Since captain (batsman) and vice-captain (bowler) must be selected , we include them first — then count valid ways to choose the remaining players abiding by the minimum batsman–bowler rule. 🔹 Step 1 — Fix the compulsory players We must include: 1 batsman (captain) 1 bowler (vice-captain) So: Players already selected = 2 \text{Players already selected} = 2 Remaining to choose: 10 − 2 = 8 10 - 2 = 8 🔹 Step 2 — Update available players After fixing the captain & vice-captain: Remaining batsmen = 7 − 1 = 6 7 - 1 = 6 Remaining bowlers = 6 − 1 = 5 6 - 1 = ...