A coin is tossed six times. How many ways can it come up heads 5 times and tails once?

Question

 please explain

 

Answer 1

The easy way to think about this problem is that, in six tosses, if only one is tails , the tails result can come up on the first toss, the second toss, the third toss, the fourth toss, the fifty toss , or the sixth toss .   This is six possibilities, so the answer to the question is 6.

 

A more sophisticated analysis is that this problem is an example of "six choose 5"  or "six choose 1"

 

 In symbols   "six choose five" is   ₆C₅ =      6! /[5! (6-5)!] = 6

                    "six choose one " is   ₆C₁  =   6!/[1! (6-1)!]   = 6