Six cards are drawn one by one from a set of unlimited number of cards, each card is marked with numbers `-1, `0` or `1`. Number of different ways in which they can be drawn if the sum of the numbers shown by them vanishes is

Options

A. `111`
B. `121`
C. `141`
D. none of these

Answer

C

Explanation

`(c )` Hence the sum of the numbers on six cards vanishes.
Case I : If selected `3` cards each of number `-1` or `1` i.e.
Number of arrangements `=(6!)/(3!3!)=20`
Case II : If selected `2` cards each of no. `-1` ,`0` or `1` i.e
Number of arrangements`=(6!)/(2!2!2!)=90`
Case III : If selected one card each of number `-1` and `1` and `4` cards of no. `0`.
No. of arrangments `=(6!)/(1!1!4!)=30`
Case IV : If all cards selected from the no. `0`
No. of arrangements `=(6!)/(6!)=1`
Hence total no. of arrangments are `20+90+30+1=141`