Consider all the possibel combinations of 3 coins using only pennies, nickels, d

Question

Consider all the possibel combinations of 3 coins using only pennies, nickels, dimes, and quaters. the total value of these combintations excceeds 6 dollars by k cents. what is the value of k

I have had others answer this question and they aaddress this as a factorial probelm by categorizing the numbers of coins with the same value within a combination. however, i feel that they are wrong. Someone said there are 3 possible combinations of coins with the same value but there are 4 coins so that does not make sense. Please help

Explanation / Answer

Total no. of combinations = C(6,3) = 20

So, the total no. of coins involved in these combinations = 20*3

No. of coins of each denomination = 60 /4
(By symmetry, we must have no. of dimes = no. of pennies)

So,
the total value = 15 * (0.01 + 0.05 + 0.10 + 0.25) = 6.15

So k=15

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