Question

In how many ways can 3 students from a class of 10 be chosen for a field trip?

Answer 1

These kind of questions have a basic thumb rule:

Whenever you have to choose and repetition is not allowed,

as in, in this case one student can not be selected more than once

also, the order of selection does not matter, that means if any three students A,B and C are selected in whatever order be ABC, ACB, BAC, BCA, CAB, CBA are counted as one kind of selection only

These kind of problem can directly be solved using Combination

Here, we can use 10C3 where 10C3 is (10 factorial / ( 3 factorial * 7 factorial ))

to calculate factorial :

n factorial = n*(n-1)*(n-2)*.....*3*2*1

S, number of ways 3 students can be chosen from a class of 10 = (10*9*8*7*6*5*4*3*2*1 / ((7*6*5*4*3*2*1)*(3*2*1))) = (10*9*8/3*2*1) = 720/6 = 120 ways