Question

Теория вероятностиВ вазе лежат 7 разных яблок и 5 различных апельсинов. Сколькими способами из них можно выбрать 3 яблока и 3 апельсина?

Answer 1

$C1= \frac{7!}{3!(7-3)!} = \frac{7!}{3!*4!} = \frac{4!*5*6*7}{3*2*4!} = \frac{5*6*7}{6}=35 \\ \\ C2= \frac{5!}{3!*(5-3)!} = \frac{5!}{3!*2!} = \frac{2!*3*4*5}{3*2*2!} =\frac{3*4*5}{3*2}=10 \\ \\ C=C1*C2=35*10=350$

ОТВЕТ:350 способов.

Answer 2

Calculating the Number of Ways to Choose 3 Apples and 3 Oranges

To calculate the number of ways to choose 3 apples and 3 oranges from a set of 7 different apples and 5 different oranges, we can use the combination formula.

The number of ways to choose 3 apples from 7 is given by the combination formula: C(n, r) = n! / (r! * (n-r)!) Where: - n = total number of items to choose from - r = number of items to choose - ! = factorial

Similarly, the number of ways to choose 3 oranges from 5 is also given by the combination formula.

Let's calculate the number of ways to choose 3 apples and 3 oranges using the combination formula.

Calculation

The number of ways to choose 3 apples from 7: C(7, 3) = 7! / (3! * (7-3)!)

The number of ways to choose 3 oranges from 5: C(5, 3) = 5! / (3! * (5-3)!)

Result

Using the combination formula, we can calculate the number of ways to choose 3 apples and 3 oranges.

C(7, 3) = 35.

C(5, 3) = 10.

Therefore, the total number of ways to choose 3 apples and 3 oranges is the product of these two combinations: Total ways = C(7, 3) * C(5, 3) = 35 * 10 = 350.