First slide

Combinations

Question

20 passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. The number of ways that they can be distributed if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck is

Moderate

A

25
B

21
C

18
D

15

Solution

Passengers refusing to sit in the lower deck (resp. upper deck) will sit in the upper deck (resp. lower deck)
$5 passengers will sit only in the lower deck and 8 passengers will sit in the upper deck.$ $Remaining passengers = 20 - (5 + 8) = 7$ Seats remaining in lower deck $= 7 - 5 = 2$
$number of ways of filling 2 seats in the lower deck = {}^{7}C_{2} = 21$
Corresponding to each choice, the remaining $5 (= 7 - 2)$ passengers will sit in the upper deck.
number of choice $= 21$

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