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Monotonically Increasing Functions

In how many w...

Question

In how many ways can a party of $4$ or more be selected from $10$ persons?

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Solution

No. of ways = $^{10} C_{4} +^{10} C_{5} +^{10} C_{6} +^{10} C_{7} +^{10} C_{8} +^{10} C_{9} +^{10} C_{10}$
$= 210 + 252 + 210 + 120 + 45 + 10 + 1$
$= 848$

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