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How many ways are there to arrange the letter in the word GARDEN with the vowels in alphabetical order? |
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Answer» The word GARDEN contains 6 letters — 4 consonants (G, R, D, N) and 2 vowels A, E. The 4 consonants can be arranged in 6 places in 6P4 ways. In each of these arrangements two places will remain blank in which the first place will be filled by A and the place following it by E as vowels have to be in alphabetical order. This can always be done in only 1 way, i.e., E following A ∴ Required number of ways = 6P4 x 1 = \(\frac{6!}{(6-4)!}=\frac{6!}{2!} \times1\) = 6 × 5 × 4 × 3 = 360. |
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