A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is
A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is
- A
$56$
- B
$21$
- C
$112$
- D
None of these
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If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{ n +1} C _{2}+2\left({ }^{2} C _{2}+{ }^{3} C _{2}+{ }^{4} C _{2}+\ldots+{ }^{ n } C _{2}\right)$ is ...... .
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- [JEE MAIN 2021]
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