Let’s think combinatorially: Among all distinct sequences of 2 R’s, 2 L’s, and 1 T, how many have all R’s before all L’s?

February 22, 2026

Let’s think combinatorially: Among all distinct sequences of 2 R’s, 2 L’s, and 1 T, how many have all R’s before all L’s?

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But since the types are indistinguishable, we count the number of ways to assign positions to the types under the constraint.
Alternative approach:
First, choose 5 positions out of 5 for placing the flowers — but since flower types have repetition, we count the number of distinct permutations where both R’s come before both L’s.
Let’s denote such sequences as valid if, in order, every R appears before every L.
We can fix the positions of the 2 R’s, 2 L’s, and 1 T, then impose the constraint that the largest R index < smallest L index.
But a more efficient method: consider the relative order of the R’s and L’s only.

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