# P/C

1) In how many ways can 5 prizes can be distributed to 8 students if each student can get any number of prizes.

a) 40 b) 5 ^{8 } c) 8 ^{5} d) None of these

2) Arjit being a party animal wants to hold as many parties as possible among his 20 friends. however,his father has warned him that he will be financing his parties under the following condition only:

a) The invitees have to be among his 20 beat friends.

b) He cannot call the same set of friends to a party more than once.

c) The number of invitees to every party have to be the same.

Given the condition ,Arjit wants to hold the maximum number of parties .How many friends should be invited to each party.

a) 11 b) 8 c) 10 d) 2

3)In how many ways 10 identical prizes can be distributed among 6 children so that each child gets atleast one present.

a) ^{15} C _{5 } b) ^{16} C _{2} c) ^{9 }C 5 _{3 } d) 6 ^{10}

4)There are three rooms in a motel: one single ,one double & one for four persons. How many ways are there to house seven persons in these rooms?

a) 7!/(1! 2! 4!) b) 7! c) 7!/3 d) 7!/3!

5) A set of 15 different words are given .In how many ways is it possible to choose a subset of not more than 5 words?

a) 4944 b)4 ^{15} c) 15 ^{4} d)4943

6) From a set of three capital consonants,five small consonant and four small vowels,how many words can be made each starting with a capital consonant and containing 3 smal consonants and two small vowels.

a) 3600 b)7200 c) 21,600 d) 28,800

7) Several teams take part in a cometition,each of which must play one game with all the other teams. How many teams took part in the competition if they played 45 games in all?

a)5 b)10 c) 15 d) 20

Answers:

1) b

2) c

3) c

4) a

5) a

6) c

7) b

n/a

Soln.

A very Important Formula:

x_{1}+x_{2}+x_{3}+...+x_{n} = A

has

(A+n-1)C(n-1) no. of solns.

Here we can write:

x1+x2+..+x6=10

But as x1>=1,...,x2>=1

Then,

let y1=x1-1y2=x2-1,...,y3=x3-1.

So eqn now becomes

x1+x2+x3+..+x6-6=10-6=4

No. of soln

(4+6-1)C(6-1)=9C5

So option (c) is correct...

Giv ur best to d world.

Nd d best will cm back to u..

Thank you specialy to you.

Regards,

Dipanjan....

n/a

Soln.:

Easy one..

Formula: Out of n items where p,q,r are identical dn no. of ways to select:

n!/(p!*q!*r!)

Here so total no. of persons=7

Identical 1,2,4.

Total ways:

7!/(1!*2!*4!)

So option (a) is correct...

Giv ur best to d world.

Nd d best will cm back to u....

Regards,

Dipanjan...

n/a

3)In how many ways 10 identical prizes can be distributed among 6 children so that each child gets atleast one present.

a) ^{15} C _{5 } b) ^{16} C _{2} c) ^{9 }C 5 _{3 } d) 6 ^{10}

simple one n-1Cc-1 so option c

Little Star

n/a

5) A set of 15 different words are given .In how many ways is it possible to choose a subset of not more than 5 words?

a) 4944 b)4 ^{15} c) 15 ^{4} d)4943

ans is 15c0+15c1+15c2+15c3+15c4+15c5=4944

Little Star

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4)There are three rooms in a motel: one single ,one double & one for four persons. How many ways are there to house seven persons in these rooms?

a) 7!/(1! 2! 4!) b) 7! c) 7!/3 d) 7!/3!

ans is (a) simple one

Little Star

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6) From a set of three capital consonants,five small consonant and four small vowels,how many words can be made each starting with a capital consonant and containing 3 smal consonants and two small vowels.

a) 3600 b)7200 c) 21,600 d) 28,800

ans is 3c1 x 5c3 x 4c2 x 5!

=21600

Little Star

n/a

7) Several teams take part in a cometition,each of which must play one game with all the other teams. How many teams took part in the competition if they played 45 games in all?

a)5 b)10 c) 15 d) 20

n(n-1)/2=45

so ans is 10

Little Star

n/a

Hey y v do take 15c0 ??

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@Shivani

Yes answer is right.

The qs demands the no. of subsets not the no. of ways..

Though I Dnt know whether that process is correct or not..

But I think

15c1+..+15c4=4933

As we know NULL SET is a subset of any set

So answer is:4933+1=4934[1 for that NULL SET]

Giv ur best to d world.

Nd d best will cm back to u....

Regards,

Dipanjan..........

n/a

1) In how many ways can 5 prizes can be distributed to 8 students if each student can get any number of prizes.

a) 40 b) 5

^{8 }c) 8^{5}d) None of thesethis one is simple one so ans is 5^8

Little Star

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