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**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