birthday for dinner

Expert replies

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Jan 27, 2010 12:02 am

A man has to invite six of his friends on his birthday for dinner. He can send invitations by post, by phone, or by his servant. In how many ways can he send invitations to his friends so that each of his friends gets only one invitation?
(A) 120
(B) 216
(C) 360
(D) 720
(E) 729

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Source: Beat The GMAT — Problem Solving | Wed Jan 27, 2010 12:02 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Jan 27, 2010 12:27 am

sanju09 wrote:A man has to invite six of his friends on his birthday for dinner. He can send invitations by post, by phone, or by his servant. In how many ways can he send invitations to his friends so that each of his friends gets only one invitation?
(A) 120
(B) 216
(C) 360
(D) 720
(E) 729

Each of the 6 friends can be invited in 3 ways, total number of ways = 3^6 = 729

Always borrow money from a pessimist, he doesn't expect to be paid back.

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Wed Jan 27, 2010 1:11 am

each person has 3 option
3*3*3*3*3*3=3^6=729

hai1: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Tue Oct 23, 2007 9:25 am; Thanked: 1 times; GMAT Score:600

by hai1 » Wed Jan 27, 2010 1:52 am

As the invitation can go only once, hence this is a permutation without repetetion.

My answer is: 6X5X4=120.

I am no expert, but this is just my answer!

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Wed Jan 27, 2010 1:57 am

hai1 wrote:As the invitation can go only once, hence this is a permutation without repetetion.

My answer is: 6X5X4=120.

I am no expert, but this is just my answer!

Letter,Letter,Letter,Letter,Letter, Servant

Is different from

Servent,Letter,Letter,Letter,Letter,Letter

and each of the 6 slots can be filled by either 1 of the 3 options (phone, letter or servant)

so the total num of ways = 3*3*3*3*3*3

Always borrow money from a pessimist, he doesn't expect to be paid back.

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