Question

Using the letters in the word TRICK a new word containing five distinct letters is formed such that T appears in the middle. The number of distinct arrangements is .............

Hint:

When one position is fixed in permutations, simply arrange the remaining letters in the remaining slots.

Answer 1

Correct Answer: 24

Step 1: Understand the condition.
The word TRICK has 5 distinct letters: T, R, I, C, K. We must form a 5-letter word using all 5 letters such that T is fixed in the middle (3rd position).
\[ \_ \ \_ \ \boxed{T} \ \_ \ \_ \] Step 2: Arrange the remaining four letters.
Remaining letters = R, I, C, K (all distinct). Number of ways to arrange 4 letters in the remaining four positions: \[ 4! = 24 \] Step 3: Conclusion.
Total distinct arrangements = 24.