From integers 1 up to 42, how many possible sets of integer are to be made if each set has six integers.

Question

assignment

Answer 1

The number of combinations of 6 digits out of 42 is 5245786.

This is 42*41*40*39*38*37/(6*5*4*3*2*1) because there are 42 ways of selecting the first integer; having selected the first integer, there are now 41 choices for the second; then 40 for the third and so on. Once the integers have been there are 6!=6*5*5*4*3*2*1 way of arranging them. We are only interested in the set so we need to reduce the number by the ways they can be arranged.