GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 22:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5  [#permalink]

### Show Tags

24 Mar 2019, 23:57
00:00

Difficulty:

75% (hard)

Question Stats:

42% (03:08) correct 58% (03:13) wrong based on 19 sessions

### HideShow timer Statistics

Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p be the probability that all four slips bear the same number. Let q be the probability that two of the slips bear a number a and the other two bear a number $$b \neq a$$. What is the value of q/p?

(A) 162
(B) 180
(C) 324
(D) 360
(E) 720

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7981
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5  [#permalink]

### Show Tags

25 Mar 2019, 06:14
1
Bunuel wrote:
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p be the probability that all four slips bear the same number. Let q be the probability that two of the slips bear a number a and the other two bear a number $$b \neq a$$. What is the value of q/p?

(A) 162
(B) 180
(C) 324
(D) 360
(E) 720

Since, we have probability out of the same set, and we have probability in both numerator and denominator, the q/p can be taken as (ways of picking two different pairs of number)/(ways of picking all four same). This will save some calculations..

Ways to choose all four - 10 *$$\frac{4!}{4!}$$, as all the numbers are similar, so 10 ways
Ways to choose two different pair - 10C2*4C2*4C2, that is (choose two out of 10), then there are 4 of each of these number, so 4C2 ways for each number)

Thus $$\frac{q}{p}=\frac{10C2*4C2*4C2}{10}=\frac{10*9*4*3*4*3}{2*2*2*10}=9*9*2=162$$
A
_________________
Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5   [#permalink] 25 Mar 2019, 06:14
Display posts from previous: Sort by