# Probability Q Exactly draws

I would like to know how to calculate the following two questions, better to have steps stated, thanks a lot.

Q1

Amy, Brenda and 4 other friends are arranged in 2 rows of 3 in order to play a game. If May and Brenda are seated next to each other, find the number of arrangements that can be made.

I would like to why the answer is not 5! x 2! = 240?

And the correct answer is 192

Q2

A box contains 4 red balls, 6 yellow balls and 5 blue balls. Alvin repeats drawing one ball at a time randomly from the box without replacement until two balls of the same colour are drawn. Find the probability that he needs exactly three draws.

So that's mean I should consider the case as follow1st time2nd time3rd timeXYYYXXBut the answer obtained is not the correct answer of 86/195

I wish to know what's wrong with my approach and why the answer is 86/195

Thousand Thanks

### 1 個解答

• wy
Lv 7
7 年前
最愛解答

Q1.

If the 6 persons are sitting in a row, the no. of ways = 2! ( Amy and Brenda interchange) x 4! ( the remaining 4 persons interchange) x 5 ( no. of ways for Amy and Brenda to sit.) = 2! x 4! x 5 = 2! x 5!.

However, if sitting in 2 rows, no. of ways that Amy and Brenda can sit together is 4 ( 2 ways in each row), not 5.

Therefore, no. of ways = 2! x 4! x 4 = 192.

Q2.

You considered only XYY and YXX, you missed out the possibility of YXY and XYX. So the answer is (86/390) x 2 = 86/195.