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From a class of 25 students, 10 are to be chosen for an excurs

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From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that their all of them will join or none of them will join. In how many ways can the excursion party be chosen?

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From a class of

25

students,

10

are to be chosen for an excursion party. There are

3

students who decide that their all of them will join or none of them will join. In how many ways can the excursion party be chosen?

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Text solutionVerified

We have 2 cases

1) when the group of

3

decides to join

Then we already have those

3

and we need to select

7

more from

22

and that can be done in

^{22} C_{7}

ways

Other case is

2) When the group of

3

decides not to join

Then we have to choose

10

from remaining

22

and that can be done in

^{22} C_{10}

ways

So total number of ways are

^{22} C_{7}

^{22} C_{10}

ways

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Question Text	From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that their all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Answer Type	Text solution:1
Upvotes	150

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that their all of them will join or none of them will join. In how many ways can the excursion party be chosen?

Text solutionVerified

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From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that their all of them will join or none of them will join. In how many ways can the excursion party be chosen?