Read the statements given below carefully.
(A) The value of \(^8C_6\) is 28.
(B) Four different people can stand in a single queue in 24 different ways.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both (A) and (B)
\(^nC_r=\,^nC_{n-r}\): choosing 6 to take is the same as choosing 2 to leave. \(n\) different people stand in a queue in \(n!\) ways.
(A) The value of \(^8C_6\) is 28 Correct.
\(\displaystyle ^8C_6=\,^8C_2=\frac{8\times7}{2\times1}=28\)
(B) Four different people can stand in a single queue in 24 different ways Correct.
Ways \(=4!=4\times3\times2\times1=24\)