These are two problems I have to solve and I just need you to check if my solution is correct. Firs

excluderho

excluderho

Answered question

2022-06-22

These are two problems I have to solve and I just need you to check if my solution is correct.
First: I have 10 red balls and 3 blue balls. What is the probability of picking 1 red ball and 3 blue balls?
My solution: 10/13 * 3/12 * 2/11 * 1/10 = 1/286
Or should it be 10/13 * 3/12 * 3/11 *3/10 = 9/572?
Second: They have 16 different postcards in the shop. How many possibilities do we have if we want to choose 6 different ones?
My solution: 16 * 15 * 14 * 13 * 12 * 11 = 5765760

Answer & Explanation

SuefsSeeltHeRn8

SuefsSeeltHeRn8

Beginner2022-06-23Added 8 answers

Your method for the first problem is the probability of selecting a red, followed by 3 blues, sequentially. We have to take into account all the different ways to arrange 3 blues and 1 red. Note that this is a hypergeometric random variable, giving probability
( 10 1 ) ( 3 3 ) ( 13 4 ) 0.014
For the second problem, your solution would be correct if ordering mattered, but it does not. Getting 123456 is considered the same as 654321. We have
( 16 6 ) = 8008

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