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by dtweah » Sun Aug 15, 2010 5:18 am
From city A to city B there are 3 different routes. From B to C there are 5. From C to D there are 2. Laxman has to go from A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete this journey if he has to take a different route while on the way back than he did while going?

A. 250

B. 90

C. 100

D. 870

E. 900
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by 4GMAT_Mumbai » Sun Aug 15, 2010 8:59 am
Hi,

Number of ways of going from A to D = 3 (A to B) times 5 (B to C) times 2 (C to D)

= 3 * 5 * 2 = 30 ways.

On his way from A to D, he could take any of these 30 routes.

On his way from D to A, he could take any of the 29 routes (apart from the route taken while going from A to D)

Hence, answer should be 30 times 29.

Hope this helps. Thanks.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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