Permutations and Combinations

[m_mayurprabhu]

Please solve this problem: -

An 8 oared boat is to be manned by a crew chosen from 11 men, of whom 3 can steer but cannot row, and the rest can row but cannot steer. In how many ways can the crew be arranged, if 2 of the men can only row on bow side?

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Mayur

[TheAkshaT]

Originally Posted by m_mayurprabhu

Please solve this problem: -

An 8 oared boat is to be manned by a crew chosen from 11 men, of whom 3 can steer but cannot row, and the rest can row but cannot steer. In how many ways can the crew be arranged, if 2 of the men can only row on bow side?

3C1 * ( 2P2 * 6P6 ) = 4320 ways!!

-Akshat

[m_mayurprabhu]

The answer is 25920 ways.

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Mayur

[voodoochild]

It is 3C1 * 6C2 * 4! * 4!

Vishal

[m_mayurprabhu]

Can you give the rationale?

Mayur

[voodoochild]

yup.. 8 oared boat will have 8 ppl to row and 1 person to steer. you can choose one person to steer in 3C1 ways. out of the 8 ppl who can row two can row only on the bow side.. you can choose the other two, out of the 6 in 6C2 ways.. finally you can arrange the rowers in 4! ways on either side... so totally you get

3C1 * 6C2 * 4! * 4!

[WIZ_Aashish]

Originally Posted by m_mayurprabhu

Please solve this problem: -

An 8 oared boat is to be manned by a crew chosen from 11 men, of whom 3 can steer but cannot row, and the rest can row but cannot steer. In how many ways can the crew be arranged, if 2 of the men can only row on bow side?

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Mayur

I am sorry but Voodochild's logic is slightly misplaced while the correct answer is that of Akshat.

Out of 11 men 3 can only steer and 8 can only row.

So various combinations for the 3 peole who will steer is 3!/2! or 3C2 = 3

Of the 8 who can only row and then with 2 of them sitting on the bow side the permutations will be 6! * 2!

Hence all the possible arrangements are 3 * 6! * 2! = 4320


Thanx for the applause (me sharing it with Akshat)

Aashish

[m_mayurprabhu]

The correct answer is that of Voodochild's. The answer is 25920 ways. That much Iam sure of the answer. There is no dispute about it. I have to examine the rationale behind Voodochild's solution which prima facie appears correct.

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Mayur

[TheAkshaT]

Originally Posted by m_mayurprabhu

The correct answer is that of Voodochild's. The answer is 25920 ways. That much Iam sure of the answer. There is no dispute about it. I have to examine the rationale behind Voodochild's solution which prima facie appears correct.

Voodoo's ans is right if the question says that 2 of them can only row from one(given) side....

Bow side means the fron of the boat so in that case my and ashish's solution is right...
as in both sides 1 person can sit at front ...

-Akshat