# A test consists of 25 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?

$3 , 268 , 760$ different ways to answer

#### Explanation:

Answer 15 only out of 25 questions then it is a combination problem.

Use nCr=(n!)/((n-r)! r!)

with $n = 25$ and $r = 15$

25C15=(25!)/((25-15)! 15!)

25C15=(25*24*23*22*21*20*19*18*17*16*cancel15!)/(10!cancel15!)

$25 C 15 = \frac{25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16}{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

$25 C 15 = 3268760$ ways

Have a nice day from the Philippines !