Only Two Fives Together

Difficulty: Hard · Topics: Discrete Mathematics, Permutations with Repetition

A piggy bank holds 3 identical 5-coin pieces, 2 identical 10-coin pieces and 4 identical 25-coin pieces. The 9 coins are laid out in a straight row so that exactly two of the 5-coin pieces are next to each other (the third is not next to them).

In how many different ways can the coins be laid out?