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  • How many distinct coins can be created by stacking 5 round coins, 4 oval coins, and 7 square coins vertically on a shelf?   Option: 1</strong

How many distinct coins can be created by stacking 5 round coins, 4 oval coins, and 7 square coins vertically on a shelf? 

 

Option: 1

1343310


Option: 2

1231442


Option: 3

1510441 


Option: 4

1441440


Answers (1)

best_answer

Given that,

There are 16 coins of different shapes.

The number of round-shaped coins = 5

The number of oval-shaped coins = 4

The number of square-shaped coins = 7

Thus, using the formula to find the number of ways the coins are arranged is given by,

\begin{aligned} & \frac{n !}{p ! \times q ! \times r !}=\frac{16 !}{5 ! \times 4 ! \times 7 !} \\ & \frac{n !}{p ! \times q ! \times r !}=4 \times 15 \times 14 \times 13 \times 12 \times 11 \\ & \frac{16 !}{5 ! \times 4 ! \times 7 !}=1441440 \end{aligned}

Therefore, the total number of ways the coins are arranged is 1441440 ways.

 

Posted by

Deependra Verma

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