Combinations

[crackthetest]

Jack is making a list of his 5 favorite cities. He will choose 3 cities from pool A with 5 in the pool. From Pool B with 3 he choose 2. How many different lists of cities ranked from first to fifth can he make?

A 30
B 360
C 1800
D 3600
E 6720

OA D

I have a doubt after calculating 5C3 and 3C2 you get 30 possible cities which could be ranked from first and fifth. So we get a permutation of 30P5, which is not listed in the choices, where am I going wrong?

[thephoenix]

Jack is making a list of his 5 favorite cities. He will choose 3 cities from pool A with 5 in the pool. From Pool B with 3 he choose 2. How many different lists of cities ranked from first to fifth can he make?

A 30
B 360
C 1800
D 3600
E 6720

OA D

I have a doubt after calculating 5C3 and 3C2 you get 30 possible cities which could be ranked from first and fifth. So we get a permutation of 30P5, which is not listed in the choices, where am I going wrong?

you r wrong we are not gvetting 30 cities but rather we are getting 30 ways in which 5 cities can be selected and then they (5 cities) can be arranged in 5! from rank 1 to 5
therfore total no. of combination is 5!*30=3600

[crackthetest]

Yes my bad.. it must be 30 possible ways of 5 cities. Thanks!