Need the multiple choice How many 6digit binary strings are

Need the multiple choice:

How many 6-digit binary strings are there with three 1\'s? (A) 20 (B) 10 (C) 1 (D) 6 How many 6-digit binary strings are there with five 1\'s?

Solution

1) A -- 3 1\'s means there should be 3 0\'s so, the total possible will be 6!/(3! x 3!)
2) C -- There are 5 1\'s means there should be 1 0, the total possible will be 6!/(5! x 1!)
3) A -- Adding the answers in questions 1&2
4) A -- Same as question 1
5) C -- Same as question 2
6) B -- 3 0\'s or 3 1\'s , both are talking about same set of strings. So the total will be only 3 0\'s.