Question

Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible ​

Answer 1

Answer:

120 Samples

Explanation:

This question is based on combinations in permutations and combinations concept.

Out of 10 we need 3 selections so we must find out 10C3

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

here n = 10 and r = 3

10C3 = 10!/(10-3)!(3!)

= 10×9×8×7×..........×3×2×1/ 7!(3!)

= 10×9×8×7!/7!(3!)

= 720 / 3!

= 720/6 = 120

10C3 = 120

therefore 120 samples are possible

Answer 2

Answer:

Number of samples possible = 120

Explanation:

We have to use combinations to determine the number of samples which are possible.

The formula for the number of such combination is

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

where n! = n(n-1)(n-2)(n-3)x_ _ _ _x(3)(2)(1)

(Note: 0! = 1)

Therefore the answer will be 10C3 = (10 × 9 × 8)/(3 × 2 × 1) = 720/6 = 120