Question

There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. How many of these sets contain any 5 numbers?

Answer 1

252 sets

Explanation:

The set given to us is:

{0,1,2,3,4,5,6,7,8,9}

Total number of elements in set = n = 10

Number of elements to be included in seach set = r = 5

As the order doesn't matter, we can use the combination formula to find number of different combinations if we choose 5 numbers from the given 10 numbers with no repetition:

C(10,5) = 10!/(5!)(10-5)!

C(10,5) = 10!/(5!)(5!)

C(10,5) = 10·9·8·7·6/ 5·4·3·2·1

C(10,5) = 252

Thus 252 sets can be formed which contains any of the 5 numbers from the sets