S-BATCH @ SRICHAITANYA: PERMUTATIONS AND COMBINATIONS TIMED

Explaination

Explanation forquestion1:

1.A cricket team of 11 players is to be selected from a group of 15 players of whom 5 are bowlers, 7 are
batsmen and 3 are all-rounders. In how many ways can the team be selected so that it should contain 3 bowlers, 6 batsmen and 2 all-roundrs?

3 bowlers can be selected from 5 in ⁵c₃ ways
6 batsmen can be selected from 7 in ⁷c₆ ways
2 all-rounders can be selected from 3 in ³c₂ ways
⁵c₃x⁷c₆x³c₂
=10x7x3=210.

Explanation for Question2:

In how many ways can 7 letters be posted in 3 letter boxes

first letter can be posted in 3 ways
second letter can be posted in 3 ways
third letter can be posted in 3 ways
fourth letter can be posted in 3 ways and so on
seventh letter can be posted in 3 ways
the answer is 3x3x3x3x3x3x3 ways.
3⁷ is the answer.

Explanation for question3:

A plane contains 10 points in which no three poins are collinear.How many triangles can be formed using these points?

To form a triangle we require 3 points. It we have to select 3 points from 10 points
therefore ¹⁰c₃

Explanation for Question 4:

If ¹⁰c₃=¹⁰c_r, then what are the possible values of r?

we knoe that ⁿc_r=ⁿc_n-r
¹⁰c₃=¹⁰c_r
r=3 or (10-3)

Explanation for Question 5:

A bag contains 5 red balls, 3 yellow balls and 2 white ball. The number of ways in which one or more balls can be taken out is

5 red balls can be choosen in 6 ways (0,1,2,3,4,5)
3 yellow balls can be choosen in 4 ways (0,1,2,3)
2 white balls can be choosen in 3 ways (0,1,2).
The no of ways possible is 6x4x3=72
atleast one ball means 72-1=71.

Explanation for Question 6:

6. Mike attempts a true or false question paper which contains 5 questions at random. The number of ways he could have answered one or more questions is

Each question can be attempted in 2 ways so, 5 questions can be attempted in 2⁵=32 ways.He has to attempt one or more questions in 32-1= 31 ways

Explanation for Question 7:

Rohan has 6 friends whom he wants to invite for dinner. The number of ways in which he can invite atleast 1 of them are

He can invite his friends in ⁶c₁+⁶c₂+⁶c₃+⁶c₄+⁶c₅+⁶c₆=63 ways.

Explanation for Question8:

In how many ways can three persons be seated in five chairs?

3 persons can be seated in 5 chairs in ⁵p₃ ways.
5x4x3=60 ways.

Explanation for Question9: A cultural committee of 8 is to be formed from 9 Asians and 5 africans. In how many ways can it be done when the committee consists of exactly three africans? A committee must consists of 3 africans and 5 asians
3 africans can be selected from 5 in ⁵c₃=10 ways
5 asians can be selected from 9 in ⁹c₅=126 ways
the answer is 10x126=1260 ways.

Explanation for Question 10:

In how many ways can a committee of 6 can be formed from 10 members so that one particular person is always included and two particular persons ar never included?

We have to select 6 from 10. But numbers never be selected it means we have to select from 8.However one particular person is always included therefore we have to select 5 from 7
In ⁷c₅ ways
⁷c₅=⁷c₂.

Explanation for Question 11:

If ⁿc₅ =ⁿc₃, find ¹⁰c_n

we know that If ⁿc_r =ⁿc_n-r
ⁿc₅ =ⁿc₃=> n=8
¹⁰c₈=45.

Explanation for Question 12:

ⁿc₀=ⁿp₀=1

Explanation for Question 13:

When 5 coins are thrown in how many ways it show exactly three tails?

then number of ways it shows exactly 3 tails is ⁵c₃ = 10.

Explanation for Question 14:

There are 12 points in a plane in which 7 points are collinear. How many straight lines can be formed by joining these points?

If There are n points in a plane in which r points are collinear. then the number of straight lines can be formed by joining these points is ⁿc₂-^rc₂+1
there fore the answer is ¹²c₂-⁷c₂+1.

Explanation for Question 15:

There are 12 points in a plane in which 7 points are collinear. How many triangles can be formed by joining these points?

If There are n points in a plane in which r points are collinear. then the number of triangles can be formed by joining these points is ⁿc₃-^rc₃
there fore the answer is ¹²c₂-⁷c₂.

Explanation for Question 16:

A number plate should have four digits.If the first digit is three, the second digit is a positive even number and the last two digits are in ascending order, then find the total number of different number plates possible.

The four number plate will be 3_ _ _,
First place can be filled in one way.
second place can be filled in 4 ways (2,4,6 and 8)
Third and fourth can be filled in
If the third digit is 0 then fourth digit can be filled in 9 ways (1,2,3,4,5,6,7,8,9)
If the third digit is 1 then fourth digit can be filled in 8 ways (2,3,4,5,6,7,8,9)
If the third digit is 2 then fourth digit can be filled in 7 ways (3,4,5,6,7,8,9)
and so on.....
If the third digit is 8 then fourth digit can be filled in 1 ways (9)
If the third digit is 9 then fourth digit can be filled in 0 ways, there is no single digit number that is greater than 9.
The third and fourth together can be filled in (9+8+7+...+1) =45 ways
The required answer is 1x4x45=180.

Explanation for Question 17:

In how many ways can six students and six teachers sit around a circular table so that no two students are sitting together?

Six teachers can be arranged by leaving one space between them in circular is 5!
Now for six students six vacant places and they can be arranged in 6! ways
The answer is 5!6!

Explanation for Question 18:

COLUMN A	COLUMN B<>
ⁿc₀	ⁿp0

QUANT COMPARISION

Five coins thrown

COLUMN A	COLUMN B
The number of ways it can show atleast 1 head	The number of ways it can show atleast 1 tail

The number of ways it shows atleast one head is equalent to the number of ways it shows atleast one tail.

Explanation for Question 19:

When two dice are thrown the number of ways it show sum atleast 11?

sum atleast 11 means it can show 11 or 12
the possible for 11 is (5,6) and (6,5)
the possible for 12 is (6,6)
The answer is 3 ways.

Explanation for Question 20:

The number of diagonal in a 12 sided polygon is

The number of diagonal in a n sided polygon is n(n-3)/2.
Therefore the required answer is 12(12-3)/2=54

S-BATCH @ SRICHAITANYA

Pages

PERMUTATIONS AND COMBINATIONS TIMED

QUANT COMPARISION

QUANT COMPARISION

Contact Form

Followers

QUANT COMPARISION