Question

Из 10 разных роз и 5 разных гербер нужно составить букет, который имеет 3 розы и 2 гербера. Сколько разных букетов можно составить?

Answer 1

C 10 3 * C 5 2 =  (10*9*8)/(1*2*3) * (5*4)/(1*2) =120*10 =1200.

* * * C 10 3 * C 5 2 = 1=  10!/(7!*3!) * 5!/ (3!*2!) * * *

Answer 2

Calculating the Number of Different Bouquets

To calculate the number of different bouquets that can be created using 10 different roses and 5 different gerberas, where the bouquet must have 3 roses and 2 gerberas, we can use the combination formula.

Step 1: Calculate the number of ways to choose 3 roses from 10 The number of ways to choose 3 roses from 10 is given by the combination formula: $$ \binom{n}{r} = \frac{n!}{r!(n-r)!} $$ where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

Step 2: Calculate the number of ways to choose 2 gerberas from 5 Similarly, the number of ways to choose 2 gerberas from 5 is calculated using the combination formula.

Step 3: Multiply the results from Step 1 and Step 2 The total number of different bouquets can be obtained by multiplying the number of ways to choose 3 roses from 10 and the number of ways to choose 2 gerberas from 5.

Calculation

Using the combination formula: - Number of ways to choose 3 roses from 10: $\binom{10}{3} = \frac{10!}{3!(10-3)!}$ - Number of ways to choose 2 gerberas from 5: $\binom{5}{2} = \frac{5!}{2!(5-2)!}$

Multiplying the results: - Total number of different bouquets = $\binom{10}{3} \times \binom{5}{2}$

Result

The total number of different bouquets that can be created using 10 different roses and 5 different gerberas, where the bouquet must have 3 roses and 2 gerberas, is the product of the two combinations calculated above.

Total number of different bouquets = $\binom{10}{3} \times \binom{5}{2}$