Question

В отделении 10 солдат и 4 сержанта. На охрану объектов необходимо выделить 8 солдат и 2 сержанта. Сколько существует вариантов составить наряд ?

Answer 1

Объяснение:

$C_{10}^8*C_4^2=\frac{10!}{(10-8)!*8!} *\frac{4!}{(4-2)!*2!} =\frac{8!*9*10}{8!*2!}*\frac{2!*3*4}{2!*2!}=9*5*3*2=270.$

Ответ: 270 вариантов.

Answer 2

10+4•8+2=140 ответ ббб

Answer 3

Calculation of Possible Combinations

To calculate the number of possible combinations for forming a squad with 8 soldiers and 2 sergeants out of a group of 10 soldiers and 4 sergeants, we can use the concept of combinations.

The number of combinations can be calculated using the formula:

C(n, r) = n! / (r! * (n-r)!)

Where: - n is the total number of soldiers (10) and sergeants (4) in the group - r is the number of soldiers (8) and sergeants (2) required for the squad

Plugging in the values, we get:

C(14, 10) = 14! / (10! * (14-10)!)

Simplifying the equation:

C(14, 10) = 14! / (10! * 4!)

Now, let's calculate the value:

C(14, 10) = (14 * 13 * 12 * 11 * 10!) / (10! * 4 * 3 * 2 * 1)

The factorial terms cancel out:

C(14, 10) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1)

Calculating the values:

C(14, 10) = 24024 / 24

Simplifying:

C(14, 10) = 1001

Therefore, there are 1001 possible combinations to form a squad with 8 soldiers and 2 sergeants out of a group of 10 soldiers and 4 sergeants.