Question

Big Bang Theory cast wishes to find out the number of ways in which the word ASTRONAUT can be scrambled. They find that the number of ways in which it can be put in an unscrambling puzzle is?

• A. 362880
• B. 181440
• C. 60480
• D. 90720

Answer 1

The Correct Option is D

The word "ASTRONAUT" has 9 letters with the letter 'A' repeated twice. The number of distinct permutations is calculated using the formula for permutations of a multiset:
\[ \frac{9!}{2!} \]
Calculating this:
\[ 9! = 362880 \]
\[ 2! = 2 \]
\[ \frac{362880}{2} = 181440 \]
Thus, the number of distinct ways to scramble the word "ASTRONAUT" is:
Answer: B (181440)