Given are all the possible 10 number combinations (NOT permutations) of the numbers 11 - 26 (8008 combinations), and 4 random numbers from the 11 - 26 sequence.
How do I find out how many of the 8008 combinations contain
a. all 4 random numbers?
b. 3 of the 4, 2 of the 4, 1 of the 4 and 0 of the 4 random numbers respectively??
(a)
There are 16 numbers from 11 to 26 inclusive.
If you set aside your four random numbers, you want to choose 6 of the remaining 12 to go with them.
There are ways to do that.
(b)
There are ways to choose 3 of the 4 random numbers.
For each of those choices there are ways to choose 7 numbers to go with them,
such that 3 of the 4 random numbers are chosen.
There are ways to choose 2 of the 4 random numbers.
There are ways to match them with 8 others that do not belong to the random numbers.
Same strategy for the remaining selections.