Compute:

Question:

Compute:

(i) $\frac{9 !}{(5 !) \times(3 !) !}$

(ii) $\frac{32 !}{29 !}$

(iii) $\frac{(12 !)-(10 !)}{9 !}$

 

 

Solution:

(i) To Find : Value of $\frac{9 !}{(5 !) \times(3 !)}$

Formulae :

$n !=n \times(n-1) !$

$n !=n \times(n-1) \times(n-2) \ldots \ldots \ldots \ldots 3 \times 2 \times 1$

Let,

$x=\frac{9 !}{(5 !) \times(3 !)}$

By using above formula, we can write,

$\therefore x=\frac{9 \times 8 \times 7 \times 6 \times(5 !)}{(5 !) \times(3 \times 2 \times 1)}$

Cancelling ( $5 !$ ) from numerator and denominator we get,

$\therefore x=\frac{9 \times 8 \times 7 \times 6}{3 \times 2 \times 1}$

$\therefore \mathrm{x}=504$

Conclusion : Hence, value of the expression $\frac{9 !}{(5 !) \times(3 !)}$ is 504 .

(ii) To Find : Value of $\frac{32 !}{29 !}$

Formula: $n !=n \times(n-1) !$

Let,

$x=\frac{32 !}{29 !}$

By using the above formula we can write,

$\therefore x=\frac{32 \times 31 \times 30 \times(29 !)}{29 !}$

Cancelling (29!) from numerator and denominator,

$\therefore \mathrm{X}=32 \times 31 \times 30$

$\therefore \mathrm{X}=29760$

Conclusion : Hence, the value of the expression $\frac{32 !}{29 !}$ is 29760 .

(iii) To Find: Value of $\frac{(12 !)-(10 !)}{9 !}$

Formula : $n !=n \times(n-1) !$

Let,

$x=\frac{(12 !)-(10 !)}{9 !}$

By using the above formula we can write,

$\therefore x=\frac{[12 \times 11 \times 10 \times(9 !)]-[10 \times(9 !)]}{9 !}$

Taking (9!) common from numerator,

$\therefore x=\frac{(9 !)[(12 \times 11 \times 10)-10]}{9 !}$

Cancelling (9!) from numerator and denominator,

$\therefore \mathrm{x}=(12 \times 11 \times 10)-10$

$\therefore \mathrm{x}=1310$

Conclusion : Hence, the value of the expression $\frac{(12 !)-(10 !)}{9 !}$ is is 1310 .

 

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