Question

$15$ Passengers are to travel by a double decked bus which can accommodate $5$ in upper deck and $10$ in lower deck. The number of ways that the passengers are distributed is

• A. $3000$
• B. $3003$
• C. $3006$
• D. $3009$

Answer 1

Answer: (B)

$3003$

Number of passenger is $15$.

Thus number of way of distribution the passengers in upper or lower deck is just the selection of $5$ or $10$ people for upper or lower deck and rest will have automatically to seat in the remaining deck.

Hence, number of ways $={}^{15}{C}_{10}$ or ${}^{15}{C}_5=3003$

Hence, option B.