Question

8!/6! 7!/2!•4!9!/6!•3!8!-7!/6!​

Answer 1

Ответ:

$\frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8}{1 \times 2 \times 3 \times 4 \times 5 \times 6} = \frac{7 \times 8}{1} = 56 \\ \frac{1 \times 2 \times 3\times 4 \times 5 \times 6 \times 7}{1 \times 2 \times 1 \times 2 \times 3 \times 4} = \frac{5 \times 6 \times 7}{2} = 15 \times 7 = 105 \\ \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 - 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7}{1 \times 2 \times 3 \times 4 \times 5 \times 6} = \frac{720(56 - 7)}{720} = 56 - 7 = 49$

Answer 2

Let's simplify the expression step by step:

1. 8!/6!

   8! (8 factorial) means 8 × 7 × 6!. So, we can simplify it as:

   (8 × 7 × 6!) / 6!

   The 6! in the numerator and denominator cancels out, leaving us with:

   8 × 7 = 56

2. 7!/2!•4!

   7! means 7 × 6 × 5 × 4!. So, we can simplify it as:

   (7 × 6 × 5 × 4!) / (2!•4!)

   The 4! in the numerator and denominator cancels out:

   (7 × 6 × 5) / 2!

   2! means 2 × 1, so we have:

   (7 × 6 × 5) / (2 × 1) = 210

3. 9!/6!•3!

   9! means 9 × 8 × 7 × 6!. So, we can simplify it as:

   (9 × 8 × 7 × 6!) / (6!•3!)

   The 6! in the numerator and denominator cancels out:

   (9 × 8 × 7) / (3!)

   3! means 3 × 2 × 1, so we have:

   (9 × 8 × 7) / (3 × 2 × 1) = 84

4. 8! - 7!/6!

   We already found 7!/6! to be 7, so:

   8! - 7

   8! means 8 × 7!, so:

   (8 × 7!) - 7

   The 7! in the first term cancels out with the 7 in the second term:

   (8 × 1) - 7 = 8 - 7 = 1

Now, let's put it all together:

56 + 210 + 84 - 1 = 349

So, the final simplified value of the expression is 349.