The binomial coefficients which are in decrea | vedclass

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(D) The binomial coefficients for $n=15$ are ${ }^{15} C_0, { }^{15} C_1, \dots, { }^{15} C_7, { }^{15} C_8, \dots, { }^{15} C_{15}$.Since ${ }^{15} C

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${ }^{15} C_7, { }^{15} C_6, { }^{15} C_5$

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(D) The binomial coefficients for $n=15$ are ${ }^{15} C_0, { }^{15} C_1, \dots, { }^{15} C_7, { }^{15} C_8, \dots, { }^{15} C_{15}$.Since ${ }^{15} C_r$ increases as $r$ increases from $0$ to $7$ and decreases as $r$ increases from $8$ to $15$,we observe the values.For option $D$,the sequence is ${ }^{15} C_7, { }^{15} C_6, { }^{15} C_5$. Since $7 > 6 > 5$ and these values are in the decreasing part of the binomial coefficient distribution (where $r > n/2$),the sequence is in decreasing order.Therefore,option $D$ is correct.

The binomial coefficients which are in decreasing order are

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