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# It is Required to Seat 5 Men and 4 Women in a Row So that the Women Occupy the Even Places. How Many Such Arrangements Are Possible? - CBSE (Arts) Class 11 - Mathematics

ConceptConcept of Combinations

#### Question

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

#### Solution

5 men and 4 women are to be seated in a row such that the women occupy the even places.

The 5 men can be seated in 5! ways. For each arrangement, the 4 women can be seated only at the cross marked places (so that women occupy the even places).

M x M x M x M x M

Therefore, the women can be seated in 4! ways.

Thus, possible number of arrangements = 4! × 5! = 24 × 120 = 2880

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 7: Permutations and Combinations
Q: 9 | Page no. 157

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Solution It is Required to Seat 5 Men and 4 Women in a Row So that the Women Occupy the Even Places. How Many Such Arrangements Are Possible? Concept: Concept of Combinations.
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