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### Permutation Combination - CAT 2016 Math Preparation

Question 4 the day: July 10, 2006

The question for the day is a sample practice problem in Permutation Combination. The problem provides an understanding of the concept of selecting 'r' things out of 'n' things.

Question:
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?
1. 1260
2. 210
3. 10C6 * 6!
4. 10C5 * 6
Correct Answer - 1260. Choice (1)

A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210*6 = 1260.

Alternatively, we can select the 5 member team out of the 10 in 10C5 ways = 252 ways.
The captain can be selected from amongst the remaining 5 players in 5 ways.
Therefore, total ways the selection of 5 players and a captain can be made = 252*5 = 1260.

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