If n is a positive integer, how does the number of combinations for nCn-1 compare to the number of combinations for nC1?

Question

ganeshie8 · Answer

hint : number of ways of choosing 1 object  = number of ways of leaving one object

ganeshie8 · Answer

does that help ha

anonymous · Answer

lol yes it did :)

ganeshie8 · Answer

suppose, u have 4 shirts, and u want to choose one shirt :
how many ways u can choose ?

ganeshie8 · Answer

from 4 shirts, u can choose 1 shirt in   4c1 =  4 ways

ganeshie8 · Answer

next, if u want to LEAVE 1 shirt and choose 3 shirts, then ho many ways u wud get ?

from 4 shirts, u can LEAVE 1 shirt in 4c3 =   4 ways

ganeshie8 · Answer

leaving 1 shirt is same as choosing 3 shirts

ganeshie8 · Answer

i mean, if you're choosing 3 shirts --- then that means you're leaving behind 1 shirt

ganeshie8 · Answer

so, in general :

$\large  ^nC_r =    ^nC_{n-r}$