Which among the following is/are not correct?

^{6} C_{2} +^{6} C_{1} =^{7} C_{2}

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^{6} C_{1} +^{6} C_{2} =^{6} C_{2}

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^{6} C_{2} +^{6} C_{1} =^{7} C_{1}

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^{6} C_{2} -^{6} C_{1} =^{7} C_{2}

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Solution

The correct options are
B $^{6} C_{1} +^{6} C_{2} =^{6} C_{2}$
C $^{6} C_{2} -^{6} C_{1} =^{7} C_{2}$
D $^{6} C_{2} +^{6} C_{1} =^{7} C_{1}$
We know that
$C (n, r) + C (n, r + 1) = C (n + 1, r + 1)$
Applying the above rule, only option (1) follows and hence options (2), (3) and (4) are correct answers.

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