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The letters of the word JOHNY can be jum...

The letters of the word JOHNY can be jumbled in 120 ways. In how many of them does the letter `H` appear in the middle?

A

1

B

`20`

C

`24`

D

`26`

Text Solution

AI Generated Solution

The correct Answer is:
To find the number of ways to arrange the letters of the word "JOHNY" such that the letter 'H' appears in the middle, we can follow these steps: 1. **Fix the position of 'H':** Since we want 'H' to be in the middle, we will place 'H' in the 3rd position of the 5-letter word. The arrangement will look like this: _ _ H _ _. 2. **Identify the remaining letters:** The remaining letters to arrange are J, O, N, and Y. 3. **Count the arrangements of the remaining letters:** We need to arrange the 4 remaining letters (J, O, N, Y) in the 4 available positions (1st, 2nd, 4th, and 5th). The number of ways to arrange these 4 letters is given by the factorial of the number of letters, which is 4!. 4. **Calculate 4!:** \[ 4! = 4 \times 3 \times 2 \times 1 = 24 \] 5. **Conclusion:** Therefore, the total number of arrangements of the letters of the word "JOHNY" with 'H' in the middle is 24. ### Final Answer: The number of ways in which the letter 'H' appears in the middle is **24**.
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