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Six cards are drawn one by one from a set of unlimited number

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

111

121

141

none

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Six cards are drawn one by one from a set of unlimited number of cards, each card is marked with numbers

- 1, 0,

1

. Number of different ways in which they can be drawn if the sum of the numbers shown by them vanishes is

8 mins ago

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8 mins ago

Text solutionVerified

Given that sum must vanish

\Rightarrow

sum

= 0

possibilities : All

0^{'} s, 3 1^{'} s

ξ

3 (- 1)^{'} s,

2 1^{'} s

2 (- 1)^{'} s

ξ

2 0^{'} s,

1 1^{'} s

1 (- 1)^{'} s

4 0^{'} s

For case

(1)

-

only

1

possible way

For case

(2)

-

\frac{6 !}{3 ! 3 !}

= 20

ways

For case

(3)

-

\frac{6 !}{2 ! 2 ! 2 !}

= 90

ways

For case

(4)

-

\frac{6 !}{4 !}

= 30

ways

Total

= 1 + 20 + 90 + 30

= 141.

Hence, the answer is

141.

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Question Text	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
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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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