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Question

Write the value of 6r=156rC3+50C4.

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Solution

6r=156rC3+50C4.

=561C3+ 562C3+ 563C3+ 564C4+ 565C5+ 566C6+ 50C4= 55C3+ 54C3+ 53C3+ 52C3+ 51C3+ 50C3+ 50C4

= 561C3+ 562C3+ 563C3+ 564C4+ 565C5+ 566C6+ 50C4= 55C3+ 54C3+ 53C3+ 52C3+ 51C3+ 50C3+ 50C4= 55C3+ 54C3+ 53C3+ 52C3+( 50C3+ 51C4)
= 55C3+ 54C3+ 53C3+ 52C3+ 51C3+( 51C3+ 51C4) {Using nCr+nCr1=n+1Cr}
= 55C3+= 54C3+( 55C3+ 54C4)= 55C3+( 54C3+ 55C4)=( 55C3+ 55C4)= 56C4
So,
6r=156rC3+ 50C4= 56C4


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