A double decked bus can accommodate 110 passengers, 50 in the upper deck and 60 in the lower deck.In how many ways can the passengers be accommodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?


A. \(\frac{85!50!60!}{40!45!}\)

B. \(\frac{85!}{40!45!}\)

C. \(\frac{110!}{50!60!}\)

D. \(\frac{110!50!60!}{40!45!}\)

E. \(\frac{110!}{40!45!}\)


Are You Up For the Challenge: 700 Level Questions
_________________

Solution

Given

• A double-decked bus can accommodate 110 passengers.

o 50 passengers in the upper deck and 60 passengers in the lower deck.
• 15 passengers refuse to be in the upper deck and 10 other passengers refuse to be in the lower deck.

To find

• The number of ways can the passengers be accommodated in the bus

.

Approach and Working out

• Total number of arrangements= Selecting and arranging 15 passengers who refuse to be in the upper deck × Selecting and arranging 10 passengers who refuse to be in the upper deck × Arranging remaining 85 passengers
• = 60C15 × 15! × 50C10 × 10! × 85!
• = \(\frac{85!50!60! }{ 40!45!}\)

The correct answer is option A.
Thus, option A is the correct answer.

Correct Answer: Option A
_________________