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 look for a sequence where the values are decreasing.Comparing the options:$A$: ${ }^{15} C_5 $B$: ${ }^{15} C_{10} $C$: ${ }^{15} C_6 $D$: ${ }^{15} C_7 > { }^{15} C_6 > { }^{15} C_5$ (Decreasing)Therefore,the sequence in decreasing order is ${ }^{15} C_7, { }^{15} C_6, { }^{15} C_5$. The correct option is $D$.

The binomial coefficients which are in decreasing order are

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