Let's solve the problem step by step.
1. Identify the Word:
The word given in number 5 on the table is "BLINDNESS".
2. Identify Consonants and Vowels:
- Consonants in "BLINDNESS": B, L, N, D, N, S, S
- Number of Consonants: 7
- Vowels in "BLINDNESS": I, E
3. Calculate Total Number of Arrangements:
The total number of ways to arrange the letters in "BLINDNESS" is the factorial of the length of the word.
- Length of the word "BLINDNESS": 9
- Total arrangements = 9! = 362,880
4. Calculate Arrangements Starting with a Consonant:
To find the number of arrangements that start with a consonant:
- First, we need to choose a consonant from the 7 consonants.
- Then, arrange the remaining 8 letters (since one consonant is already chosen and fixed at the first position).
- So, total arrangements starting with a consonant = 7 8!
5. Calculate 8!:
- 8! = 40,320
6. Multiply:
- Total arrangements starting with a consonant = 7 40,320 = 282,240
So, the number of different arrangements of the letters in "BLINDNESS" that start with a consonant is:
282,240
