Question

Find the number of permutations and combinations which can be made by taking four items at a time from six given distinct items, without repetition.

• A. $360,20$
• B. $360,15$
• C. $400,25$
• D. $372,18$

Answer 1

The correct option is B $360,15$

Given that there are $6$ items $\xi$ we need to choose only $4$ at a time without repeating.

$1st$ Item can be chosen from any of the $6,$

$2nd$ Item from any of the remaining $5$ and so on.

$\Rightarrow$ Total Permutations $=6\times 5\times 4\times 3={}^6{P}_4=360.$

$\Rightarrow$ Total Combinations $=\frac{{}^6{P}_4}{4!}={}^6{C}_4=15.$

Hence, the answer is $360,15.$