Restricted Speakers

Probability Level 3

There are 10 girls and 8 boys in a class room including Mr. Deepanshu Gupta , Mrs. Pranjal Jain and Ms. Amrita Roychowdhury.

A list of speakers consisting of 8 girls and 6 boys has to be prepared.

Mr. Deepanshu refuses to speak if Mrs. Pranjal is speaker.

Mrs. Pranjal refuses to speak if Ms. Amrita is a speaker.

What is the number of ways the list can be prepared?

202 952 308 567

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U Z by U Z , 24, Guyana

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1 solution

Discussions for this problem are now closed

Pranjal Jain
Nov 5, 2014

A m r i t a P r a n j a l D e e p a n s h u Number of ways Y N − ( 8 7 ) ( 8 6 ) = 224 N Y N ( 8 7 ) ( 7 6 ) = 56 N N − ( 8 8 ) ( 8 6 ) = 28 \begin{array}{lcr} \mbox Amrita & Pranjal & Deepanshu & \text{Number of ways} \\ \mbox Y & N & - & \binom{8}{7}\binom{8}{6}=224 \\ \mbox N & Y & N & \binom{8}{7}\binom{7}{6}=56 \\ \mbox N & N & - & \binom{8}{8}\binom{8}{6}=28 \\ \end{array}

These are three possible cases. So total possible ways are 224+56+28= 308 \boxed{308}

Note:

  • Y = Selected ; N = Not selected ; - = May be selected
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