OPERATIONS WITH FACTORIALS PERMUTATION AND COMBINATION

Evaluate the following

Problem 1 :

(a) 6!

Solution:

6! = 6 × 5 × 4 × 3 × 2 × 1

= 720

(b) 10!

Solution:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 3628800

(c) 11!

Solution:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 39916800

(d) ⁵P₂ 

Solution:

(e) ¹²P₄

Solution:

(f) ²⁰P₅

Solution:

(g) ⁶C₂

Solution:

(h) ¹²C₅

Solution:

Evaluate the following

Problem 2 :

(a) ⁵P₅

Solution:

(b) ¹⁰⁰P₄

Solution:

(c) ¹⁰C₁₀

Solution:

(d) ¹⁰⁰C₂

Solution:

(e) ¹⁰⁰¹C₉₉₉

Solution:

Problem 3 :

Show that ²⁰C₆ = ²⁰C₁₄

Solution:

Problem 4 :

Evaluate:

(i) ⁴P₂

Solution:

(ii) ⁶P₃

Solution:

(iii) ⁴P₃/³P₂

Solution:

(iv) ⁶P₃ × ⁵P₂

Solution:

(v) ⁿP_n

Solution:

Problem 5 :

Verify each of the following statements:

(i) 6 × ⁵P₂ = ⁶P₂

Solution:

6 × ⁵P₂ = ⁶P₂

So, the given statement is false.

(ii) 4 × ⁷P₃ = ⁷P₄

Solution:

4 × ⁷P₃ = ⁷P₄

So, the given statement is true.

(iii) ³P₂ × ⁴P₂ = ¹²P₄

Solution:

³P₂× ⁴P₂ = ¹²P₄

So, the given statement is false.

(iv) ³P₂ + ⁴P₂ = ⁷P₄

Solution:

³P₂ + ⁴P₂ = ⁷P₄

So, the given statement is false.