Think Binomial

( 10 3 ) + ( 11 3 ) + ( 12 3 ) + ( 13 3 ) + ( 14 3 ) + ( 15 3 ) + ( 16 3 ) + ( 17 3 ) + ( 18 3 ) + ( 19 3 ) + ( 20 3 ) {10\choose3} + {11\choose3} + {12\choose3} + {13\choose3} + {14\choose3} + {15\choose3} + {16\choose3} + {17\choose3} + {18\choose3} + {19\choose3} + {20\choose3} Calculate the above sum.

This is part of the set My Problems and THRILLER


The answer is 5775.

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2 solutions

Akhil Bansal
Aug 1, 2015

Hint : To apply the property ( n r ) {n \choose r} + ( n r + 1 ) {n \choose r+1} = ( n + 1 r + 1 ) {n+1 \choose r+1}
Just add and subtract ( 10 4 ) {10 \choose 4} ,now simply apply the above formula,you will get the answer.

Ankit Kumar Jain
Aug 1, 2015

hockey stick identity.

I Gede Arya Raditya Parameswara - 3 years, 5 months ago

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