Probability of rolled die

Question

If a fair die is rolled 7 times, what is the probability , to the nearest thousandth, of getting exactly 2 ones

Answer 1

roll a fair die 7 times

what is the probability of exactly two 1's?

P(0 ones) =7C0 (5/6)^7

P(1 one) = 7C1(1/6)(5/6)^6

P(2 ones) = 7C2(1/6)^2(5/6)^5

= (7!/2!5!)(5^5)/(6^7)

= 21(3125)/279936

= about .234429

= 23.4429% probability of exactly 2 ones on 7 rolls of a fair die

or is that true? that's the probability of exactly 2 of a kind, 2 ones, 2 twos, 2 threes, 2 fours, 2 fives or 2 sixes in 7 rolls of the die. so should we divide by 6 to get just the probability of 2 ones? that would mean 23.4429/6 = .0390714

= 3.907% for exactly two ones