1. Three numbers are chosen from 1,2,3,4,5,6,7,8,9. Find the number of arrangements in which the smallest chosen numbers is odd.
Ans (Highlight to find out) : 300

2. Find the number of ways in which 10 people can be divided into
(a) 3 groups consisting of of 2,3, and 5 people
(b) 2 groups consisting of 3 people each and a group of 4 people
(c) 5 groups of 2 people each
Ans: (a)2520 (b)2100 (c)945

Thanks

2. Originally Posted by irake
1. Three numbers are chosen from 1,2,3,4,5,6,7,8,9. Find the number of arrangements in which the smallest chosen numbers is odd.
Ans (Highlight to find out) : 300

Mr F says: Number of arrangements with:

(1 and two other numbers) + (3 and two other numbers greater than 3) + (5 and two other numbers greater than 5) + (7 and two other numbers greater than 7) = 3[(1)(8)(7) + (1)(6)(5) + (1)(4)(3) + (1)(2)(1)] = 3(100) = 300.

2. Find the number of ways in which 10 people can be divided into
(a) 3 groups consisting of of 2,3, and 5 people

Mr F says: $\displaystyle {10 \choose 2} \, {8 \choose 3} \, {5 \choose 5} = ......$.

(b) 2 groups consisting of 3 people each and a group of 4 people

Mr F says: $\displaystyle \frac{{10 \choose 3} \, {7 \choose 3} \, {4 \choose 4}}{2!} = ......$.

(c) 5 groups of 2 people each
Ans: (a)2520 (b)2100 (c)945

Mr F says: $\displaystyle \frac{{10 \choose 2} \, {8 \choose 2} \, {6 \choose 2} \, {4 \choose 2} \, {2 \choose 2}}{5!} = ......$.

Thanks
But why hide the answers ......?

3. Ah, I was thinking that maybe you would like to do it yourself first before looking at the answer =\

I guess my logic was a bit warped, for the first qns, I tried:
(All odd) + (1 odd 2 even) + (2 odd 1 even)=
(All odd) + ((odd n0 is 1) + (odd no is 3)+...+(odd no is 7)) + ((smaller odd no is 1)....)
That's where I got messed up. The second question I was wondering if it was permutations or combi, and got even more messy

4. Originally Posted by irake
Ah, I was thinking that maybe you would like to do it yourself first before looking at the answer =\

I guess my logic was a bit warped, for the first qns, I tried:
(All odd) + (1 odd 2 even) + (2 odd 1 even)=
(All odd) + ((odd n0 is 1) + (odd no is 3)+...+(odd no is 7)) + ((smaller odd no is 1)....)
That's where I got messed up. The second question I was wondering if it was permutations or combi, and got even more messy
Well, I hope it's all blue sky now