NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 40
Total: 41
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Solution:
Total no. of students = 25
No. of students chosen for an excursion party = 10
Now 3 students decided either they are all join the party or none of them will join.
When all 3 of them will join the party then we have to choose 7 more students out of 22.
Then no. of ways =
C 7
When all 3 of them will not join the party then we have to choose 10 students out of 22.
Then the no. of ways =
C 10
∴ Required no. of ways =
C 7 +
C 10
No. of students chosen for an excursion party = 10
Now 3 students decided either they are all join the party or none of them will join.
When all 3 of them will join the party then we have to choose 7 more students out of 22.
Then no. of ways =
When all 3 of them will not join the party then we have to choose 10 students out of 22.
Then the no. of ways =
∴ Required no. of ways =
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