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There are 21 people on a team. How many different ways can 5 of them be selected to be captains?Do not include commas in your answer. For example, 1,000 should be entered as 1000.
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In this scenario we have 21 people on a team and were asked how many different ways can five of them be selected to be captains? Now this is a question of combinations, not permutations, because if we just want to have five captains, it doesn't really matter the order of the captain. If they're all just equal captains, it's just a group of five people. The only question is which five? You know, it's not as if they have to be standing in a certain order or something. So the answer is there are 21, choose five ways to select five captains, that 21 people. So I'm not sure if in your course you've become familiar with this notation, which is and choose our so it's the number of combinations of size are from a group of size. In this is equal to and factorial divided by R. Factorial times and minus R. Factorial. So for our question we have 21 Choose five, 21 21 factorial By five factorial divided by 16 factorial. And this comes out to 20,000 349. So that's how many ways we can make five captains from a team of
In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?
This question was previously asked in
NDA [Held On: 18 Apr 2021] Maths Previous Year paper
View all NDA Papers >
- 42
- 35
- 21
- 20
Answer [Detailed Solution Below]
Option 3 : 21
Free
Electric charges and coulomb's law [Basic]
10 Questions 10 Marks 10 Mins
Concept:
Combination Formula
nCr = \[\rm \frac{n!}{r! [n - r]!}\]
Calculation:
A particular player should not be included
We have to select 5 players from [8 - 1] = 7 players.
⇒ required number of ways = 7C5
\[⇒ \frac{7!}{5! [7-5]!}\] = 21
∴ The required number of ways is 21.
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