Permutations and Combinations - doubt

The question appears to be erroneous / incomplete / answer choices are wrong - what is the source of this question?
As is, the answer should be: 461 possible ways to select a com. of 5 with at least 1 g from 5 bs and 6 gs.

BUT if you edit the question to read: "A committee of 5 is to be selected from among 5 boys and 6 girls. In how many ways can this be done if the committee is to consist of at-least one girl and at least one boy?
A) 105 B) 225 C) 230 D) 350 E) 455

Such questions need to be structured in two parts:
1. List the number of possible ways in which the selection (committee) can be composed
Then the possible selection / composition of committee = 1g & 4b (one girl and 4 boys in the committee, and so on), 2g & 3b, 3g & 2b, 4g & 1b

2. Find the number of combination counts possible for each selection.
1g & 4b => 6C1 *5C4 = 6*5 = 30 possible ways (Use combination formula)
2g & 3b => 6C2 *5C3 = 15*10 = 150 possible ways
3g & 2b => 6C3 *5C2 = 20*10 = 200 possible ways
(Note: From a GMAT perspective, you can stop here because the sum of the above 3 = 380 and hence the answer must be E. 455 which is the only value > 380)
4g & 1b => 6C4 * 5C1 = 15*5 = 75 possible ways

Total possible ways = [spoiler]30 + 150 + 200 + 75 = 455[/spoiler]
Hence E.

krishnaprasad wrote:A committee of 5 is to be selected from among 5 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
A) 105
B) 225
C) 230
D) 350
E) 455

what is the answer choice and how?

Also, you can think as follows: we have to choose 5 from among 11 people. This can done in 11C5=11*10*9*8*7/5! = 462 ways

One of these comittees have 5 boys and 6C5=6 of these comittees have 5 girls

krishnaprasad wrote:A committee of 5 is to be selected from among 5 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
A) 105
B) 225
C) 230
D) 350
E) 455

what is the answer choice and how?

Also, you can think as follows: we have to choose 5 from among 11 people. This can done in 11C5=11*10*9*8*7/5! = 462 ways

One of these comittees have 5 boys and 6C5=6 of these comittees have 5 girls