Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

In how many ways can a Quality Analyst team of 10 members be made from 18 experts such that 5 English experts must never be included in the team?
Option: 1
$1360$

Option: 2
$1162$

Option: 3
$1287$

Option: 4
Cannot be determined

Answers (1)

best_answer

Note the following:

The formula for the combination for the selection of the $\mathrm{ x}$ items from the $\mathrm{ y}$ different items is $\mathrm{ ={ }^y \mathrm{C}_x=\frac{y !}{x !(y-x) !} }$

The restricted combination for the selection of the $\mathrm{ r }$ items from the $\mathrm{ n }$ different items with $\mathrm{ \mathrm{k} }$ particular things always excluded is $={ }^{\mathrm{n}-\mathrm{k}} \mathrm{C}_{\mathrm{r}}$

Since 5 English experts must never be included in the Quality Analyst, the following is evident.

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

$\mathrm{=n-k=18-5=13.}$

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

$\mathrm{=r-k=10-5=5}$

Therefore, the required restricted combination is

$\mathrm{ ={ }^{n-k} \mathrm{C}_{\mathrm{r}} }$
$\mathrm{ ={ }^{13} \mathrm{C}_5 }$

$\mathrm{=\frac{13!}{8!5!}}$

$\mathrm{=1287}$

Posted by

Devendra Khairwa

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: NTA exam city intimation slip link available; admit card date

anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads

anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26

Latest Question