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Chapter 7 Permutations and Combinations Ex-7.4 Interview Questions Answers

Question 1 : If nC8 = nC2,find nC2.

Answer 1 :

Question 2 :

Determine n if
(i) 2nC3:nC3 = 12: 1
(ii) 2nC3nC3 = 11:1

Answer 2 :


Simplifying andcomputing

 4 × (2n – 1) =12 × (n – 2)

 8n – 4 = 12n –24

 12n – 8n = 24 –4

 4n = 20

 n = 5

 11n – 8n = 22 –4

 3n = 18

 n = 6

Question 3 : How many chords can be drawn through 21 points on a circle?

Answer 3 :

Given 21 points on a circle
We know that we require two points on the circle to draw a chord
∴ Number of chords is are
 21C2=
 
∴ Total number of chords can be drawn are 210

Question 4 : In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Answer 4 :

Given 5 boys and 4girls are in total

We can select 3 boysfrom 5 boys in 5C3 ways

Similarly, we canselect 3 boys from 54 girls in 4C3 ways

 Number of ways ateam of 3 boys and 3 girls can be selected is 5C3 × 4C3

 5C3 × 4C3 =

 5C3 × 4C3 = 10 ×4 = 40

Number of ways a teamof 3 boys and 3 girls can be selected is 5C3 × 4C3 =40 ways

Question 5 : Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Answer 5 :

Given 6 red balls, 5white balls and 5 blue balls

We can select 3 redballs from 6 red balls in 6C3 ways

Similarly, we canselect 3 white balls from 5 white balls in 5C3 ways

Similarly, we canselect 3 blue balls from 5 blue balls in 5C3 ways

 Number of waysof selecting 9 balls is 6C3 ×5C3 × 5C3

 Number of waysof selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if eachselection consists of 3 balls of each colour is 6C3 ×5C3 × 5C3 =2000

Question 6 : Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Answer 6 :

Given a deck of 52cards

There are 4 Ace cardsin a deck of 52 cards.

According to question,we need to select 1 Ace card out the 4 Ace cards

 Number of waysto select 1 Ace from 4 Ace cards is 4C1

 More 4 cards areto be selected now from 48 cards (52 cards – 4 Ace cards)

 Number of waysto select 4 cards from 48 cards is 48C4

 Number of 5 cardcombinations out of a deck of 52 cards if there is exactly one ace in eachcombination 778320.

Question 7 : In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Answer 7 :

Given 17 players inwhich only 5 players can bowl if each cricket team of 11 must include exactly 4bowlers

There are 5 playershow bowl, and we can require 4 bowlers in a team of 11

 Number of waysin which bowlers can be selected are: 5C4

Now other players leftare = 17 – 5(bowlers) = 12

Since we need 11players in a team and already 4 bowlers are selected, we need to select 7 moreplayers from 12.

 Number of wayswe can select these players are: 12C7

 Total number ofcombinations possible are: 5C4 × 12C7

 Number of wayswe can select a team of 11 players where 4 players are bowlers from 17 playersare 3960

Question 8 : A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Answer 8 :

Given a bag contains 5black and 6 red balls

Number of ways we canselect 2 black balls from 5 black balls are 5C2

Number of ways we canselect 3 red balls from 6 red balls are 6C3

Number of ways 2 blackand 3 red balls can be selected are 5C2× 6C3

 Number of waysin which 2 black and 3 red balls can be selected from 5 black and 6 red ballsare 200

Question 9 : In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Answer 9 :

Given 9 courses areavailable and 2 specific courses are compulsory for every student

Here 2 courses arecompulsory out of 9 courses, so a student need to select 5 – 2 = 3 courses

 Number of waysin which 3 ways can be selected from 9 – 2(compulsory courses) = 7 are 7C3

 Number of ways astudent selects 5 courses from 9 courses where 2 specific courses arecompulsory are: 35


Selected

 

Chapter 7 Permutations and Combinations Ex-7.4 Contributors

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