A school team has 9 volleyball players. A 6 member team and a captain will be selected out of these nine players. How many different selections can be made?a)24b)112c)252d)288e)168Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Selecting captain from 9 members is 9C1.
selecting other 6 members from remaining 8 is 8C6.
thus total selection is 9C1*8C6=252

Answer

Answer

Explanation:

Total number of ways to select a 6 member team:
- To select a 6 member team out of 9 players, we can use the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n = total number of players = 9, r = number of players to be selected = 6
- Calculating C(9, 6):
C(9, 6) = 9! / (6!(9-6)!)
= 9! / (6!3!)
= (9 * 8 * 7) / (3 * 2 * 1)
= 84

Total number of ways to select a captain:
- Once the 6 member team is selected, there are 6 players left.
- The captain can be any one of these 6 players.
- So, the number of ways to select a captain from the 6 member team is 6.

Total number of different selections:
- To find the total number of different selections, we multiply the number of ways to select a 6 member team with the number of ways to select a captain.
- Total number of different selections = 84 * 6 = 504
Therefore, the correct answer is not among the options provided.

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