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  • Suppose you have 8 relative cards for your friends and you want to send them to 4 of your relatives. In how many ways can you send these cards to 4 of your relatives?<div class='qna-o

Suppose you have 8 relative cards for your friends and you want to send them to 4 of your relatives. In how many ways can you send these cards to 4 of your relatives?

Option: 1

1240


Option: 2

2320


Option: 3

1680


Option: 4

3260


Answers (1)

best_answer

Here we have to find the number of permutations of 4 objects out of 8 objects.


In other words, we have to count the number of permutations of 8 objects taking 4 at a time.


The number of ways is given by,

            \begin{aligned} { }^8 P_4 & =\frac{8 !}{(8-4) !} \\ { }^8 P_4 & =\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{4 \times 3 \times 2} \\ { }^8 P_4 & =8 \times 7 \times 6 \times 5 \times 4 \\ { }^8 P_4 & =1680 \end{aligned}

Therefore, the number of ways the card is sent is 1680 ways.

Posted by

Deependra Verma

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