Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In how many ways can Alok choose 15 colours from a box of 25 colours such that red, yellow, green, blue must always be included?Option: 1 <

In how many ways can Alok choose 15 colours from a box of 25 colours such that red, yellow, green, blue must always be included?

Option: 1

\frac{25!}{11!10!}


Option: 2

\frac{25!}{15!10!}


Option: 3

\frac{21!}{11!15!}


Option: 4

\frac{21!}{11!10!}


Answers (1)

Note the following:

  • The formula for the combination for the selection of the \mathrm{x} items from the \mathrm{y}different items is \mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}

  • The restricted combination for the selection of the \mathrm{r} items from the \mathrm{n}different items with \mathrm{k} particular things always included is \mathrm{=^{n-k}C_{r-k}}

Since 4 colours must always be included, the following is evident.

  • The number from which the restricted combination is to be made is

          =\mathrm{n-k=25-4=21}.

  • The number with which the restricted combination is to be made is

          \mathrm{=r-k=15-4=11}

Therefore, the required restricted combination is

=\mathrm{^{n-k}C_{r-k}}

\mathrm{=^{21}C_{11}}

=\frac{21!}{11!10!}

Posted by

Sumit Saini

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question