A college has 10 basketball players. A 5 member team and a captain will be…
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A college has 10 basketball players. A 5 member team and a captain will be selected out of these 10 players. How many different selections can be made?
Answer: C. 1260 — Answer: 1260 Step 1: Choose the 5-member team from the 10 players. This can be done in C(10,5) = 252 ways. Step 2: Choose the captain from the selected 5…
- A.
1230
- B.
1200
- C.
1260
- D.
1500
Attempted by 40 students.
Show answer & explanation
Correct answer: C
Answer: 1260
Step 1: Choose the 5-member team from the 10 players. This can be done in C(10,5) = 252 ways.
Step 2: Choose the captain from the selected 5 players. This can be done in 5 ways.
Total ways = 252 × 5 = 1260.
Alternate method: choose the captain first (10 ways) and then choose the remaining 4 team members from the other 9 players: 10 × C(9,4) = 10 × 126 = 1260, which gives the same result.
Note: The original solution arrived at the correct final number but used incorrect wording (it said selecting a team of 6). The corrected explanation above selects a 5-member team and then a captain, matching the problem statement.