Question

How many 4-digit numbers can be formed using digits 1 to 6 if the digit 4 is never there in the number and the repetition of digits is not allowed?

• A. 116
• B. 118
• C. 120
• D. 124

Hint:

For non-repeating digit problems: \[ ^nP_r = \frac{n!}{(n - r)!} \] Here, exclude restricted digits first, then apply permutation.

Answer 1

The Correct Option is C

Step 1: Identify the digits allowed.
Digits given: \( \{1, 2, 3, 4, 5, 6\} \) \(\Rightarrow\) Total digits = 6
Digit 4 is not allowed, so remaining digits = \( \{1, 2, 3, 5, 6\} \) \(\Rightarrow\) 5 digits Step 2: Count valid 4-digit numbers.
We have to form 4-digit numbers using 5 digits (excluding 4), without repetition. So, total such numbers = Number of 4-digit permutations from 5 digits: \[ ^5P_4 = 5 \times 4 \times 3 \times 2 = 120 \]