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In how many different ways can a coach distribute 3 prizes (gold, silv
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14 Aug 2023, 00:23
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In how many different ways can a coach distribute 3 prizes (gold, silver, and bronze) to 3 players out of 10 players so that John, who is one among the 10 players, gets a prize?
Re: In how many different ways can a coach distribute 3 prizes (gold, silv
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02 Oct 2023, 03:19
1
Carcass wrote:
In how many different ways can a coach distribute 3 prizes (gold, silver, and bronze) to 3 players out of 10 players so that John, who is one among the 10 players, gets a prize?
This is fairly easy. First, let's recognise that the order matters. Then, Coach wants John to be one of the winners, so finding the other two winners= 9*8. Because we don't know whether John will win a Gold or a Silver or a Bronze, total no. of ways = 9*8*3 = 216.
Re: In how many different ways can a coach distribute 3 prizes (gold, silv
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09 Oct 2023, 01:03
1
Since the order matters in given scenario, there are 3 possibilities in which John will get a prize. 1. John gets a Gold -> 1 * 9C1 * 8C1 2. John gets a silver -> 9C1 * 1 * 8C1 3. John gets a Bronze -> 9C1*8C1*1
Lastly, adding all the possibilities - 3*9*8 = 216
In how many different ways can a coach distribute 3 prizes (gold, silv
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18 Jan 2024, 07:17
1
First we find out how many groups of \(3\) players out of \(10\) can be formed and then decide how many ways we can give each of these groups of three players, Gold, Silver and Bronze prizes.
Now, since John always gets a prize, he must always be in the group of \(3\) players.
So we need to find out the number of ways we can select \(2\) players out of \(9\) players
Number of groups \(= \frac{9!}{2! \times 7!} = \frac{9 \times 8 \times 7!}{2 \times 7!} = \frac{9 \times 8}{2} = 36\)
There are \(36\) possible groups of \(3\) players each.
Within each group, we can distribute the Gold, Silver and Bronze prizes to the three players in \(3!\) or \(6\) different ways.
For \(36\) groups, we can distribute the prizes in \(36 \times 6 = 216\) ways.
gmatclubot
In how many different ways can a coach distribute 3 prizes (gold, silv [#permalink]