Algebra

Binomial Theorem

Properties of Binomial Coefficients

         

What positive integer nn satisfies (n+211)=109(n9)?{{n+2} \choose 11}=109 \cdot {n \choose 9}?

Caroline has 417417 coins, no two of which are the same. The number of ways she can choose 8989 of these coins is the same as the number of ways she can choose kk of these coins for some k>89.k > 89. What is the value of k?k?

What is the arithmetic mean of the following sereis: (80),(81),(82),,(88)?{ 8 \choose 0 }, { 8 \choose 1 }, { 8 \choose 2 }, \cdots, { 8 \choose 8 }?

What is the value of positive integer nn satisfying (26n)=(26n4)?{26 \choose n}={26 \choose {n-4}}?

If (n+42)+(n+32)=25,{n+4 \choose 2}+{n+3 \choose 2}=25, what is the value of n?n?

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