If N=the number of coins, then N≠1, because no single coin has a value of 30c. Let the number of nickels=n, number of dimes=d, number of quarters=q.
q=0 or 1; d=0, 1, 2, or 3; n=0, 1, 2, 3, 4, 5, or 6. The total value of the coins=30=25q+10d+5n. We can divide this equation by 5:
5q+2d+n=6. This is an easier equation to work with.
If q=d=0 then n=6, 6 nickels.
If q=0, then 2d+n=6, that is, 2d=6-n or d=3-n/2.
So n must be even:
n=0, d=3, 3 dimes.
n=2, d=2, 2 dimes and 2 nickels.
n=4, d=1, 1 dime and 4 nickels.
n=6, d=0, 6 nickels.
If q=1, then 2d+n=1, that is, n=1-2d, so d=0 and n=1 is the only solution: 1 quarter and 1 nickel.
Count the number of red statements: 6 ways to make up 30c.