The value of
$(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :
- $2^{21} - 2^{10}$
- $2^{20} - 2^{9}$
- $2^{20} - 2^{10}$
- $2^{21} - 2^{11}$
The Correct Option is C
Solution and Explanation
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JEE Main Notification
Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.