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Home » 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?
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?
CBSE | Class 11 | Maths | Miscellaneous Exercise | NCERT | Permutations and Combinations
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?

In this question we get 2 options that is

(i) Either all 3 will go

Then remaining students in class are:

    \[25\text{ }-\text{ }3\text{ }=\text{ }22\]

Number of students remained to be chosen for party

    \[=\text{ }7\]

Number of ways choosing the remaining 22 students

    \[\Rightarrow {{~}^{22}}{{C}_{7}}=\]

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Image 54

(ii) None of them will go

The students going will be 10

Remaining students eligible for going

    \[=\text{ }22\]

Number of ways in which these 10 students can be selected are

    \[^{22}{{C}_{10}}\]

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Image 55

Total numbers of ways in which students can be chosen are

    \[=\text{ }170544\text{ }+\text{ }646646\text{ }=\text{ }817190\]

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