Question

Из 10 роз и 8 лилий нужно составить букет, содержащий 2 розы и 3 лилии. Сколько можно составить различных букетов?

Answer 1

 

C_10^2 из роз(С с индексом 10 и в степени2)

C_8^3 из лилий

C_10^2*C_8^3=(10!/2!*8!) *(8!/3!*5!)= (1*2*3*4*5*6*7*8*9*10/1*2*1*2*3*4*5*6*7*8)*( 1*2*3*4*5*6*7*8/1*2*3*1*2*3*4*5)= (9*10/1*2)*( 6*7*8/1*2*3)=2520

 

Answer 2

Calculation of Different Bouquets

To calculate the number of different bouquets that can be made using 10 roses and 8 lilies, we need to determine the number of ways we can choose 2 roses and 3 lilies from the total number of flowers available.

The formula to calculate the number of combinations is given by:

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

Where: - n is the total number of items (roses + lilies) - r is the number of items to be chosen (2 roses + 3 lilies) - ! denotes the factorial operation

Let's calculate the number of different bouquets:

C(10+8, 2+3) = (18!)/(5! * 13!)

Using a calculator or a programming language, we can calculate the result.