Untitled 7 (7)

'Fin'} ffce ooeffirient of ar²⁰ in (j" + x* + ar³ + .r⁴ + x ')(. •* + / 4- .r⁴ + .. .)*•

6.    l’se generating functions to find the nuniber of ways to seleit 10 bali from a large pile ol red, wbite and blue balls if:

a)    the seleetion ha.s at least two balls of eaeh color.

b)    the seleetion has at least two red balls.

7.    Find the uiunber of ways to seleet 1,2,3,4,5.6,7,8.0,1 fruits from a p le of 3 apples, 5 o ran ges and 2 banatias. (Hint: Use generatiug functions)

s. How many ways are there to ilivide '2 blue, 5 red ant 0 wbite balls nto two etptal unortlereil piles '!

9. Show tliat :

a)    I i.+>h — f' , 7''_m -f /*n—|f*n—2,

b)    (Fn)² — F_n+,F_n-\ = (-l)\

where F„ are the Fibouacci nuntbers.