No. of ways of putting coins in pockets

The 9 coins can be put in the pockets as-
1) 9 in 1 pocket,0 in the other
2) 8 in 1 pocket,1 in the other
3) 7 in 1 pocket,2 in the other
4) 6 in 1 pocket,3 in the other
5) 5 in 1 pocket,4 in the other

Ans - (i) 5

If the coins are different,

For 1)#ways - ⁹C₀

For 2)#ways - ⁹C₁

For 3)#ways - ⁹C₂

For 4)#ways - ⁹C₃

For 5)#ways - ⁹C₄

Ans - (ii)⁹C₀+⁹C₁+⁹C₂+⁹C₃+⁹C₄ = 2⁹/2 = 2⁸