Four friends A,B,C and D are celebrating Christmas together. More info:


label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Following presents left to unwrap:one  from A, three from B and three from C. How many ways to arrange these presents in the form of a circle if no two presents from person B can be placed one next to another?

Nov 18th, 2017

total 7 presents can be used to form circle in (7-1)! ways = 6! ways

out of which 3 gifts of can be together so  we need to find the way in which all the gifts can be placed next to each other = (5-1)! = 4! ways
and 3 gifts can arrange themselves in 3! ways.

and 2 gifts can be considered as 1 and can be arranged in = (6-1)! = 5! ways
and 2 gifts can arrange themselves in = 2! ways

so the no. of ways = 6! - [(4!*3!) + (*5!*2!)]

= 720- [(24*6)+(120*2)]
=720-[144+240] = 336 ways (answer)


Please best my answer. Thanks :)


Dec 27th, 2014

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