Question

C^4 10= C^6 10= 10!/4!(10-4!)= 4•5•6•7•8•9•10/4!•12•3•4•5•6=7•2•3•5=210

Answer 1

$C_{10}^4=\frac{10\cdot 9\cdot 8\cdot 7}{4!}=\frac{10\cdot 9\cdot 8\cdot 7}{1\cdot 2\cdot 3\cdot 4}=10\cdot 3\cdot 7=210\\\\C_{10}^6=C_{10}^{10-6}=C_{10}^4=210$

Или:  $C_{10}^4=\frac{10!}{4!\, \cdot \, 6!}=\frac{6!\, \cdot 7\cdot 8\cdot 9\cdot 10}{4!\, \cdot \, 6!}=\frac{7\cdot 8\cdot 9\cdot 10}{1\cdot 2\cdot 3\cdot 4}=210$  .

Answer 2

It seems you're performing a series of calculations involving factorials and multiplication. Let's break down each step to understand the process:

1. C^4 10: It appears that "C^4" refers to the combination function, denoted as "C," and "10" indicates the value you're taking the combination of. C^4 10 means finding the number of combinations of 10 objects taken 4 at a time. This can be calculated using the formula: C(n, r) = n! / (r!(n-r)!). Substituting the values, C^4 10 = 10! / (4!(10-4)!) = 10! / (4!6!).

2. C^6 10: Similar to the previous step, C^6 10 means finding the number of combinations of 10 objects taken 6 at a time. Using the combination formula, C^6 10 = 10! / (6!(10-6)!).

3. 10!/4!(10-4!): Here, you're calculating the value of 10 factorial divided by 4 factorial times the factorial of (10-4). In other words, it represents the number of ways to arrange 10 objects with 4 objects fixed in place (order matters).

4. 4•5•6•7•8•9•10/4!•12•3•4•5•6: This step seems to involve multiplying a sequence of numbers and dividing by another sequence. It appears to be related to the previous step's calculation, but the values in the numerator and denominator don't align correctly. It might be necessary to clarify this part of the calculation.

5. 7•2•3•5 = 210: This is a simple multiplication of the given numbers, resulting in the value 210.

Please provide more information or clarification if you need assistance with a specific step or if there are additional calculations you would like to perform.