# A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?

A. 11340

B. 12750

C. 40

D. 320

**Answer: Option A **

__Solution(By Examveda Team)__

There 10 questions in part A out of which 8 question can be chosen as = ^{10}C

_{8}

Similarly, 5 questions can be chosen from 10 questions of Part B as =

^{10}C

_{5}

Hence, total number of ways,

$$\eqalign{ & { = ^{10}}{{\text{C}}_8}{ \times ^{10}}{{\text{C}}_5} \cr & = \frac{{10!}}{{2! \times 8!}} \times \frac{{10!}}{{5! \times 5}} \cr & = \left\{ {10 \times \frac{9}{2}} \right\} \times \left\{ {\frac{{10 \times 9 \times 8 \times 7 \times 6}}{{5 \times 4 \times 3 \times 2 \times 1}}} \right\} \cr & = 11340 \cr} $$

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## Comments ( 2 )

Related Questions on Permutation and Combination

A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

D. 8! 4! 4!

A. 7560,60,1680

B. 7890,120,650

C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

C. 7 × 9!

D. 9 × 8!

Why is multiply not adding at the end ?

Wrong answer...

11340 is the right one