5 person enter an empty railway carriage in which there are 8 seats-4 facing engine and 4 with their backs to engine?

Irene

2020-08-08 10:16 pm

In how many ways they can take their seats if:
a)two particular persons X and X sit facing engine(1440)

b)X sits in a corner(3360)

c)X sits with his back to the engine while Y sits facing the engine(1920)

Answers are in the brackets.

Thanks

回答 (1)

micatkie

2020-08-08 11:14 pm

✔ 最佳答案

a)
Firstly, the 2 particular persons take 2 seats facing engine out of 4 seats (₄P₂).
Secondly, the other 3 persons take 3 seats out of 6 seats left (₆C₃).

No. of ways
= ₄P₂ × ₆C₃
= 12 × 120
= 1440

====
b)
Firstly, X takes 1 seat in a corner out of 4 seats (₄P₁).
Secondly, the other 4 persons take 4 seats out of the 7 seats left (₇P₄).

No. of ways
= ₄P₁ × ₇P₄
= 4 × 840
= 3360

====
c)
Firstly, X takes 1 seat back to the engine out of 4 seats (₄P₁).
Second, Y takes 1 seat facing the engine out of 4 seats (₄P₁).
Thirdly, the other 3 persons take 3 seats out of the 6 seats left (₆P₃).

No. of ways
= ₄P₁ × ₄P₁ × ₆P₃
= 4 × 4 × 120
= 1920

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