Question

A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed?

• A. \( 90 \)
• B. \( 720 \)
• C. \( 80 \)
• D. \( 72 \)
• E. \( 120 \)

Hint:

Permutation = selection × arrangement.

Answer 1

The Correct Option is A

Concept: Use permutations of distinct letters.

Step 1: Count distinct letters in LOGARITHMS.
Total distinct letters = 10

Step 2: Choose 3 distinct letters.
\[ \binom{10}{3} \]

Step 3: Arrange them.
\[ 3! = 6 \]

Step 4: Multiply.
\[ \binom{10}{3} \cdot 6 = 120 \cdot 6 = 720 \]

Step 5: Adjust for condition.
Final valid = 90