Question

Write the following products in factorial notation: 

(i) 6 × 7 × 8 × 9 × 10 × 11 × 12 

(ii) 3 × 6 × 9 × 12 × 15

Answer 1

: (i) Formula : n! = n x (n-1) x (n-2) ..... 3 x 2 x 1

Let, 

x = 12 x 11 x 10 x 9 x 8 x 7 x 7 x 6

Let, Multiplying and dividing by (5 x 4 x 3 x 2 x 1)

From the above formula, 

x = \(\frac{12!}{5!}\)

Conclusion :

∴ (12 x 11 x 10 x 9 x 8 x 7 x 6) = \(\frac{12!}{5!}\) 

(ii) Formula : n! = n x (n - 1) x (n-2) ....3 x 2 x 1

Let,

x = 3 x 6 x 9 x 12 x 15 

Above equation can be written as