Question

А)15!*7!/22!*3! б)5!-10!/5!

Answer 1

1) 15!7!/22!3!=(4*5*6)/(16*17*18*19*20*21*22)=1/(3*16*17*19*21*22)
2) (5!-10!)/5! = (5!(1-6*7*8*9*10)/5! = 1-6*7*8*9*10

Answer 2

To simplify the expressions, let's evaluate each one separately:

a) 15! * 7! / 22! * 3!

To simplify this expression, we can cancel out common terms in the numerator and denominator.

First, let's look at the factorial terms:

15! / 22! = (15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

In the numerator, we can cancel out the common terms with the denominator:

(15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

This simplifies to:

1 / (22 * 21 * 20 * 19 * 18 * 17 * 16)

Now let's look at the factorial terms:

7! / 3! = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)

In the numerator, we can cancel out the common terms with the denominator:

(7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)

This simplifies to:

(7 * 6 * 5 * 4) / (3 * 2 * 1)

Now we can substitute these simplified terms back into the original expression:

(1 / (22 * 21 * 20 * 19 * 18 * 17 * 16)) * ((7 * 6 * 5 * 4) / (3 * 2 * 1))

Calculating the numerical value:

(1 / (22 * 21 * 20 * 19 * 18 * 17 * 16)) * ((7 * 6 * 5 * 4) / (3 * 2 * 1)) ≈ 0.0000003217

So, the value of a) 15!*7!/22!*3! is approximately 0.0000003217.

b) 5! - 10!/5!

Let's evaluate this expression step by step:

5! = 5 * 4 * 3 * 2 * 1 = 120

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800

Now, substitute these values into the expression:

5! - 10!/5! = 120 - (3,628,800 / 120)

Calculating the division:

10!/5! = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1) = 30,240

Substituting back into the expression:

5! - 10!/