The letters of the word LUCKNOW are arranged among themselves. Find the probability of always having NOW in the word.
Question
The letters of the word LUCKNOW are arranged among themselves. Find the probability of always having NOW in the word.
Solution
Step 1: Consider "NOW" as a single entity. So, the word LUCKNOW becomes LUC(NOW).
Step 2: The total number of ways to arrange the letters in LUC(NOW) is 6!. This is because there are 6 entities now (L, U, C, K, N, and NOW), and the number of ways to arrange n entities is n!.
Step 3: However, within the entity NOW, the letters can be arranged in 3! ways.
Step 4: So, the total number of ways to arrange the letters in LUCKNOW, always having NOW together, is 6! * 3!.
Step 5: The total number of ways to arrange the letters in LUCKNOW, without any restrictions, is 7!. This is because there are 7 letters in LUCKNOW.
Step 6: The probability of always having NOW together is therefore (6! * 3!) / 7!.
Step 7: Simplify the expression to get the final probability.
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