When rolling 10 dice with 2020 faces each (numbered 1 to 20), how many ways are there of rolling a total sum of 15?

Here is all of the ways to get 15 out of 10 dice: 1*9+6=15 1*8+2+5=15 1*8+3+4=15 1*7+2*2+4=15 1*7+2*3+2=15 1*6+2*3+3=15 1*5+2*5=15

How many ways are there to answer a 20-question exam where 15 questions are true-false and 5 questions are multiple choice with 4 choices each?

There are 5 mangoes and 6 bananas. In how many different ways can a selection of fruits be made if all fruits of same kind are numbered with different tags.