# Question 10:

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

Answer:Population = 10

No. of possible samples are 30 (=10 × 3)

This answer is wrong... please corelate your answers

3 has to be selected out of 10.

we can select any combination of 3 students out of 10.

formula for combination is

${}^{n}C_{r}=\frac{n\iota}{\left(n-r\right)\iota *r\iota},wheren\iota =n*n-1*n-2*n-3*......$

n is the total number of observations and r is the number of observations which is to be selected.

here, n = 10

r = 3

${}^{10}C_{3}=\frac{10\iota}{\left(10-3\right)\iota *3\iota}=\frac{10*9*8*7\iota}{7\iota *3\iota}=\frac{10*9*8}{3*2*1}\phantom{\rule{0ex}{0ex}}=120ways\phantom{\rule{0ex}{0ex}}$

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