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There are 7 participants in a race of 400m. In how many ways can 3 dif

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There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post Updated on: 17 Apr 2018, 01:40
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Question Stats:

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Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #2

There are 7 participants in a race of 400m. In how many ways can 3 different prizes be distributed to the top 3 winners?

Options:
A. 35
B. 140
C. 210
D. 280
E. 300

Learn to use the Keyword Approach in Solving PnC question from the following article:


Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

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Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:18.
Last edited by EgmatQuantExpert on 17 Apr 2018, 01:40, edited 4 times in total.
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There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post Updated on: 17 Apr 2018, 08:56

Solution



Given:
    • 7 runners are participating in the race of 400m.

To find:
    • The number of top 3 winners can get the prizes.

Approach and Working:

    • We need to first select the 3 winners among the 7 participants and then arrange the prizes among them.
      o Thus, this is a permutation question.
    • Hence, 3 different prizes can be given to top 3 winners in 7p3=210 ways.

Hence, option C is the correct answer.

Answer: C
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Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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Originally posted by EgmatQuantExpert on 11 Apr 2018, 23:20.
Last edited by EgmatQuantExpert on 17 Apr 2018, 08:56, edited 1 time in total.
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Re: There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post 11 Apr 2018, 23:49
EgmatQuantExpert wrote:
Learn structured approach to identify permutation and combination question - Exercise Question #3

There are 7 participants in a race of 400m. In how many ways can 3 different prizes be distributed to the top 3 winners?

Options:
A. 35
B. 140
C. 210
D. 280
E. 300



Since there are 7 participants, the 3 different prizes can be distributed as follows:

There are 7 ways of distributing the first prize. Similarly, there are 6 ways
and 5 ways of distributing the second and third prizes respectively.

Therefore, there are 7*6*5 = 210 ways(Option C) in which the different prizes can be distributed.
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Re: There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post 11 Apr 2018, 23:51
EgmatQuantExpert wrote:
Learn structured approach to identify permutation and combination question - Exercise Question #3

There are 7 participants in a race of 400m. In how many ways can 3 different prizes be distributed to the top 3 winners?

Options:
A. 35
B. 140
C. 210
D. 280
E. 300


7C3*3! --> 7!/(4!3!)*3! = 210 --> option C.

imo, answer is option C.
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Re: There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post 13 Apr 2018, 00:36
Selecting top 3 winners out of 7 participants in 7C3 ways.

Now the first winner has the opportunity to get any 1 out 3 prizes. Hence 3 options.
Similarly the second one has 2 and the last one has 1.

Therefore, 7C3*3*2*1=210.
IMO C.
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Re: There are 7 participants in a race of 400m. In how many ways can 3 dif  [#permalink]

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New post 17 Apr 2018, 09:03
Hey everyone,

The official solution to the question has been posted. :-)

Regards,
Ashutosh
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Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

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Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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Re: There are 7 participants in a race of 400m. In how many ways can 3 dif &nbs [#permalink] 17 Apr 2018, 09:03
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