Compute \(\frac{8!}{6!\times2!}\)

Question

Number of seven digits numbers which can be formed by using all the digits 1, 2, 3, 4, 5 with at least one digit repeated is _____.

Answer 1

Given:

8! / (6! × 2!)

Step 1: Expand factorials

8! = 8 × 7 × 6!

2! = 2 × 1 = 2

Step 2: Substitute and simplify

8! / (6! × 2!)

= (8 × 7 × 6!) / (6! × 2)

Cancel 6!:

= (8 × 7) / 2

= 56 / 2

= 28

Final Answer:

8! / (6! × 2!) = 28

Solution and Explanation