In How many ways can 4 people be seated in a row containing 5 seats?

1.	In How many ways can 4 people be seated in a row containing 5 seats?
Answer» To find : Number of ways in which 4 people can be seated in a row containing 5 seats. The possible number of ways in which 4 people be seated in a row containing 5 seats = ⁷P₄ (There are 5 places to be filled with 4 persons where arrangement doesn’t matter.) \(7^P_4=\frac{7!}{(7-4)!}\) .....\(\Big(nP_r=\frac{n!}{(n-r)!}\Big)\) = \(\frac{7!}{3!}\) =7 × 6 × 5 × 4 = 840

Answer»

To find : Number of ways in which 4 people can be seated in a row containing 5 seats.

The possible number of ways in which 4 people be seated in a row containing 5 seats = ⁷P₄

(There are 5 places to be filled with 4 persons where arrangement doesn’t matter.)

\(7^P_4=\frac{7!}{(7-4)!}\) .....\(\Big(nP_r=\frac{n!}{(n-r)!}\Big)\)

= \(\frac{7!}{3!}\)

=7 × 6 × 5 × 4

= 840

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