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.

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

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

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?

Pradeep

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

## 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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