The binomial coefficients which are in decreasing order are

• A

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

  ${ }^{15} C_{10},{ }^{15} C_9,{ }^{15} C_8$
• C

  ${ }^{15} C_6,{ }^{15} C_7,{ }^{15} C_8$
• Correct answer
  D

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

Solution

The series of binomial coefficient is ${ }^{15} C_0,{ }^{15} C_1,{ }^{15} C_2 \ldots{ }^{15} C_7,{ }^{15} C_8,{ }^{15} C_9 . .{ }^{15} C_{14},{ }^{15} C_{15}$
Form the above discussion, we can say that decreasing series is ${ }^{15} C_7,{ }^{15} C_6,{ }^{15} C_5$ therefore option (4) is correct.

Hence, the correct answer is option: 'D'.