Find the number of these permutations in which(i) the letters O and R are together, in the word HISTORY
Question
Solution
Sure, here are the steps to find the number of permutations in which the letters O and R are together in the word HISTORY:
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First, consider the letters O and R as a single entity. So, the word HISTORY becomes HISTY(OR). Now, we have 6 entities to arrange, which are H, I, S, T, Y, and (OR).
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The number of ways to arrange these 6 entities is 6!, which equals 720.
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However, within the entity (OR), O and R can be arranged in 2! ways, which equals 2.
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Therefore, the total number of permutations in which O and R are together is 6! * 2! = 720 * 2 = 1440.
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