Permutation and CombinationHard
Question
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
Solution
Here the sum of the numbers are vanishes of six cards i.e
Case I : If selected 3 cards each of number - 1 or 1 i.e
The number of arrangement =
= 20
Case II : If selected 2 cards each of no. - 1, 0 or 1 i.e
number of arrangement =
= 90
Case III : If selected one card each of number -1 and 1 and 4 cards of no. 0.
so no. of arrangement is
= 30
Case IV : If all cards selected fram the no. 0
So no. of arrangement is
= 1
Hence total no. of arrangement is 20 + 90 + 30 + 1 = 141
Case I : If selected 3 cards each of number - 1 or 1 i.e
The number of arrangement =
= 20Case II : If selected 2 cards each of no. - 1, 0 or 1 i.e
number of arrangement =
= 90Case III : If selected one card each of number -1 and 1 and 4 cards of no. 0.
so no. of arrangement is
= 30Case IV : If all cards selected fram the no. 0
So no. of arrangement is
= 1Hence total no. of arrangement is 20 + 90 + 30 + 1 = 141
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