Question

2.15. В коробке 10 гвоздик – 5 белых и 5 красных. Продавщица цветочного киоска вынимает 6 случайных гвоздик из коробки, чтобы украсить ими витрину. С какой вероятностью в коробке останется 1 красная и 3 белых гвоздики?

Answer 1

Если продавщица вынит 4красных и 2белых гвоздики

Answer 2

Problem Analysis

In this problem, we are given a box containing 10 carnations, 5 white and 5 red. The florist randomly selects 6 carnations from the box to decorate the storefront. We need to find the probability that there will be 1 red carnation and 3 white carnations left in the box.

Solution

To solve this problem, we can use the concept of combinations. The total number of ways to choose 6 carnations from a box of 10 is given by the combination formula:

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

Where n is the total number of carnations in the box and r is the number of carnations chosen.

In our case, n = 10 and r = 6. So, the total number of ways to choose 6 carnations from the box is:

C(10, 6) = 10! / (6!(10-6)!) = 210

Now, let's calculate the number of ways to choose 1 red carnation and 3 white carnations from the box. We have 5 red carnations and 5 white carnations in the box. So, the number of ways to choose 1 red carnation from 5 and 3 white carnations from 5 is:

C(5, 1) * C(5, 3) = (5! / (1!(5-1)!)) * (5! / (3!(5-3)!)) = 5 * 10 = 50

Therefore, the probability that there will be 1 red carnation and 3 white carnations left in the box is:

P = (Number of ways to choose 1 red and 3 white carnations) / (Total number of ways to choose 6 carnations)

P = 50 / 210 = 5/21

So, the probability that there will be 1 red carnation and 3 white carnations left in the box is 5/21.

Answer

The probability that there will be 1 red carnation and 3 white carnations left in the box is 5/21.