# Rita puts 9 pairs of black socks and 8 pairs of white socks in a drawer. She takes 3 socks. What is the probability that we get a pair of black socks?

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#### s

• Sep 9th, 2005

9C3

#### arnab kr

• Jan 25th, 2006

among 3 socks she has to choose 2 black socks from 9 pair(=18) of black socks, that can be done in 18C2 ways. and the third sock can be chosen from among the remaining socks that can be done in ((8+9-1)x2 )C 1 ways i.e. in 32 ways.

ans. 32 X 18C2

#### shweta narayan

• Jun 19th, 2006

i am interested in these materials ..kindly help

#### Partha006 Profile Answers by Partha006

• Jun 30th, 2006

Rita puts 9 pairs of black socks and 8 pairs of white socks in a drawer. She takes 3 socks. What is the probability that we get a pair of black socks?

The probablity is 9c2/17c3

#### sri

• Nov 10th, 2006

its 32C1/34C3

#### purushotham

• Nov 12th, 2006

#### suman

• Nov 13th, 2006

we can get a pair of black socks in two ways3 black socks or 2 black and 1 white socksso probability is(18C3+18C2*16C1)/34C3

#### prathyusha

• Nov 28th, 2006

its (18C2 * 32C1)/34c3

#### Balu Vasudevan Pillai

• Sep 26th, 2007

Answer should be  9C1/17C1, that is probability to draw a pair.

#### ganeshbhat Profile Answers by ganeshbhat

• Feb 17th, 2010

There are two ways in which a pair of black socks can be picked.
1) All three are black : No. of ways of doing it is 18c3
2) Two black and one white: No. of ways of doing this is 18c2*16c1

Hence total No. of ways of picking a pair of black socks is : 18c3+(18c2*16c1)
Total No. of ways any 3 socks can be picked=(18+16)C3 =34C3
Hence the probability of picking a pair of black socks=(18c3+(18c2*16c1)) / 34C3

#### skumar06cs Profile Answers by skumar06cs

• Jul 21st, 2010

9 pairs means 18 shocks and similarly 8 pairs equivelent to 16..
3 black shocks can be chosen in 2 ways which is as follows
18c3  or 18c2 and 16c1
Sample space =34c3
so the required answer will be = [18c3+(18c2*16c1)]/34c3

#### Mahesh Maka Profile Answers by Mahesh Maka

• Feb 15th, 2011

First we should find number of socks inside the drawer ie(9*2)+(8*2)= 34

pro=(18c2*16c1)/34c3=40.9090%

#### prititripathi Profile Answers by prititripathi

• Feb 20th, 2011

probability is 1 coz out of 3 atleast 2 will b of same color

#### namrata

• Nov 16th, 2011

6/11

#### Ravi

• Jan 27th, 2012

1/2

#### TUSHAR ANIL GULVE

• Jan 28th, 2012

8

#### abhishek

• Sep 6th, 2012

18C2*(16C1+16c1)/34C3

#### RAJALAKSHMI

• Feb 21st, 2013

6/11

#### Rupesh kumar

• Jul 20th, 2014

18C3+18C2*16C1/34C3
=6/11

#### Raj choudhary

• Sep 27th, 2015

Please tell me what happens if she choose 2 black socks which are from different pairs.

#### rashmi

• Mar 29th, 2016

9c1/(17c1*32c1) => denominator should comprise of all the possibilities..right?

• Apr 20th, 2016

1/2

#### Amit

• Mar 31st, 2017

The correct answer will be ( 9C1 * 32C1 ) / 34C3
This is because, pair means left and right side socks so it wont be 18C2 in place of 9C1

#### Sheetal boity

• Apr 5th, 2017

(9+8)=17
=9/17
=8/17

#### sridhar

• May 23rd, 2017

21/170

#### Anjali

• Aug 18th, 2017

we have to pick pair of black and white
the combination is (BBW,BWB,WBB from socks rack)
chance for getting BBW: 18/34*17/33*16/32 = 9/66
chance of getting BWB = 18/34*16/33*17/32 = 9/66
chance of getting WBB = 16/34*18/33*17/32 = 9/66
Probability of getting pair of black ang white socks = WBB+BBW+BWB = 3*9/66 = 9/22