 In this session we will discuss a question which says that if 16C0, 16C1, 16C2 and so on up to 16C16 with the coefficients in the expansion 1 plus x whole raise to power 16, 16C1 plus 16C3 plus 16C5 and so on up to 16C15 is equal to 16C0 plus 16C2 plus 16C4 plus so on up to 16C16. Now before starting the solution of this question we should know a result. And that is 1 plus x whole raise to power n is equal to mC0 plus mC1 into x plus mC2 into x square plus so on up to mCn into x raise to power n where the value of x is less than 1. Now this result will work out as a key idea for solving out this question. And now where we start with the solution? Here for expanding 1 plus x whole raise to power 16 we will use the result which is given in the key idea. So this will be equal to 16C0 plus 16C1 into x plus 16C2 into x square plus so on up to 16C16 into x raise to power 16. Now let us put x is equal to minus 1. Then we get 1 plus minus 1 whole raise to power 16 is equal to 16C0 plus 16C1 into minus 1 plus 16C2 into minus 1 square plus so on up to 16C16 into minus 1 whole raise to power 16. This implies 1 minus 1 whole raise to power 16 is equal to C0 minus 16C1 plus 16C2 minus 16C3 plus 16C4 plus so on up to 16C16. Now this implies 0 is equal to 16C0 minus 16C1 plus 16C2 minus 16C3 plus 16C4 and so on up to 16. Now shifting negative terms on one side and positive terms on the other side this implies 16C1 plus 16C3 plus so on up to 16C15 is equal to 16 plus 16C2 plus 16C3 plus 16 so on up to 16C15 is equal to 16C0 plus 16C2 minus 16C4 plus 16C3 plus 16C1. plus 16C4 plus so on up to 16C16. Thank you for your question and that's all for this session. Hope you all have enjoyed the session.