Question

The number of 7 letter words (with or without meaning) starting with the letter B that can be formed using the letters of the word BIOLOGY is .............. (answer in integer)

Hint:

When calculating arrangements of letters with repeated characters, divide by the factorial of the number of repetitions to account for indistinguishable arrangements.

Answer 1

Step 1: Understanding the problem.
We need to form 7-letter words starting with the letter B from the word "BIOLOGY". The available letters in "BIOLOGY" are: B, I, O, L, O, G, Y. The task is to form a 7-letter word starting with "B".
Step 2: Considering the positions of letters.
Since the word must start with "B", the remaining 6 positions can be filled with the remaining letters: I, O, L, O, G, Y.
The number of possible words is determined by how many different ways we can arrange the remaining 6 letters: I, O, L, O, G, Y. Notice that there are 2 O's, so the number of distinct arrangements is: \[ \frac{6!}{2!} \] Step 3: Calculating the number of arrangements.
First, calculate \( 6! \) and \( 2! \): \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \] \[ 2! = 2 \times 1 = 2 \] Now, calculate the number of distinct arrangements: \[ \frac{6!}{2!} = \frac{720}{2} = 360 \] Final Answer: \[ \boxed{360} \]