In how many ways the letter of the word "RAINBOW" can be arranged such that A must come before I, and I must come before O?
2026-03-29 11:48:34.1774784914
In how many ways the letter of the word "RAINBOW" can be arranged such that A must come before I, and I must come before O?
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Hint: look at the problem as if you have 4 boxes _A_I_O_ where I put the dashes. Now can you figure out in how many ways you can place the remaining 4 letters in these boxes ( $C(4,4) $)? In the end you get $4!C(4,4)$ one for each permutation of the letters.
Each box can fit 0-4 letters and since we take all 4! permutations the order in which the letters are placed doesn’t matter.