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# There are total 10 balls in a jar , 8 of them are unique and 9th and

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Manager
Joined: 13 Aug 2018
Posts: 74
There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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Updated on: 29 Feb 2020, 13:13
5
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:22) correct 35% (02:23) wrong based on 20 sessions

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There are total 10 balls in a jar , 8 of them are unique and 9th and 10th ball both have same color. In how many ways can we pick 5 balls from the jar if same color balls are not allowed in the 5 balls set?

a. 170
b. 196
c. 182
d. 252
e. 186

can someone explain this problem ? Thanks

Originally posted by jackfr2 on 26 Feb 2020, 03:10.
Last edited by jackfr2 on 29 Feb 2020, 13:13, edited 1 time in total.
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Re: There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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26 Feb 2020, 07:19
1
jackfr2 wrote:
There are total 10 balls in a jar , 8 of them are unique and 9th and 10th ball both have same color. In how many ways can we pick 5 balls from the jar if same color balls are not allowed in the 5 balls set?

a. 170
b. 196
c. 182
d. 252
e. 186

can someone explain this problem ? Thanks

Total Ways to pick 5 out of 10 balls = 10C5 = 252

Ways to pick 5 balls so that same color balls are always in selected group of 5 balls = 8C3 = 56

Favorable cases = 252 - 56 = 196

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Re: There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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Updated on: 26 Feb 2020, 15:08
Repeated ((

Tks
See below

Originally posted by newyork2012 on 26 Feb 2020, 08:44.
Last edited by newyork2012 on 26 Feb 2020, 15:08, edited 1 time in total.
Manager
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Re: There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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26 Feb 2020, 08:57
Correct me if my understanding is wrong . Thanks

What about when only one of the two is chosen ..... they are exactly the same ,but when you use c10,5 , you actually calculate c84 twice

Imagine if they were different ... we would use c21*c84 ... this is a part of the c10,5

My approach :
Since the two are the same ... it’s the same as to choose 5 out 9.....C95 = 126
Or C84+C85=126

Or C10,5-C83-C84=126

GMATinsight wrote:
jackfr2 wrote:
There are total 10 balls in a jar , 8 of them are unique and 9th and 10th ball both have same color. In how many ways can we pick 5 balls from the jar if same color balls are not allowed in the 5 balls set?

a. 170
b. 196
c. 182
d. 252
e. 186

can someone explain this problem ? Thanks

Total Ways to pick 5 out of 10 balls = 10C5 = 252

Ways to pick 5 balls so that same color balls are always in selected group of 5 balls = 8C3 = 56

Favorable cases = 252 - 56 = 196

Posted from my mobile device[/quote]
Manager
Joined: 03 Aug 2015
Posts: 82
Location: India
Concentration: Finance, Operations
GMAT 1: 720 Q49 V38
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Re: There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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Updated on: 29 Feb 2020, 13:10
newyork2012

As tempting as it may sound, 9C5 is not the correct approach. It completely disregards the arrangments made by 4 (out of 8 unique) balls with the 10th ball.

Originally posted by Sparta_750 on 29 Feb 2020, 12:54.
Last edited by Sparta_750 on 29 Feb 2020, 13:10, edited 3 times in total.
Manager
Joined: 03 Aug 2015
Posts: 82
Location: India
Concentration: Finance, Operations
GMAT 1: 720 Q49 V38
WE: Consulting (Consulting)
Re: There are total 10 balls in a jar , 8 of them are unique and 9th and  [#permalink]

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29 Feb 2020, 13:03
Another approach in addition to the one mentioned by GMATinsight

(B)

Total cases: 10 C 5 = 252

Probability of both picking ball 9= 1/10, probability of picking ball 10 = 1/10

So if we are picking 5 balls, probability of ball 9 or ball 10 to be picked or excluded each is= 1/10* 5 = 1/2

Since probability is 1/2, ball 9 or ball 10 would be selected in half the cases (from 252) and when either of them would be selected the other one would also be included in4 /9 cases (4 spots for the remaining 9 balls) that we must exclude.

All in all total cases

252-252*1/2*4/9= 252-56= 196

GMATinsight wrote:
jackfr2 wrote:
There are total 10 balls in a jar , 8 of them are unique and 9th and 10th ball both have same color. In how many ways can we pick 5 balls from the jar if same color balls are not allowed in the 5 balls set?

a. 170
b. 196
c. 182
d. 252
e. 186

can someone explain this problem ? Thanks

Total Ways to pick 5 out of 10 balls = 10C5 = 252

Ways to pick 5 balls so that same color balls are always in selected group of 5 balls = 8C3 = 56

Favorable cases = 252 - 56 = 196

Posted from my mobile device
Re: There are total 10 balls in a jar , 8 of them are unique and 9th and   [#permalink] 29 Feb 2020, 13:03