Latest Gate Aptitude Question SOLUTION: Ravi has 5 friends.In how many ways can he invite one or more of them to a dinner? option i. 31 ii. 5^5 iii. 13 iv. 2^5

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(#M40030554) GATE Numerical Ability question Permutation Keep an EYE

Ravi has 5 friends.In how many ways can he invite one or more of them to a dinner?
option
i. 31
ii. 5^5
iii. 13
iv. 2^5

Asked In Gate Sakshi (10 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Anchuri Sandeep Reddy  (10 years ago)

When he want to call only one friend no of ways =5
when he wants to call two frnds, no of ways he can call=5c2=10
when he wants to call three frnds, no of ways he can call=5c3=10
when he wants to call four frnds, no of ways he can call=5c4=5
when he wants to call five frnds, no of ways he can call=5c5=1

so totally he can call one or more frnds in (5+10+10+5+1)=31 ways.

Is this solution Helpfull? Yes (9) | No (1)  

Mahesh  (10 years ago)

Here, for every friend Ravi has two options,

Either inviting the friend or not inviting the friend

So, for every friend there are two options, for five friends he has
2*2*2*2*2 = 32 ways.

But, in these 32 ways, we even considered the possibility of not inviting any of the five friends.
That particular possibility should be deducted from the list.

So, the answer will be 32 - 1 = 31
Answer is 31

Is this solution Helpfull? Yes (5) | No   

Sakshi  (10 years ago)

: he may invite one or more friends by selecting either one or two or three or four or five friends out of five friends.
Therefore, 1 friend can be selected out of 5 in 5c1 ways
2 friend can be selected out of 5 in 5c2 ways
3 friend can be selected out of 5 in 5c3 ways
4 friend can be selected out of 5 in 5c4 ways
5 friend can be selected out of 5 in 5c5 ways
5c1+5c2+5c3+5c4+5c5=31

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Siba Kumar Sahu  (10 years ago)

ans:
No of ways:-
when he calls 1 friend = 5c1
2 friends = 5c2
3 friends = 5c3
4 friends = 5c4
5 friends = 5c5
total no of ways=5c1+5c2+5c3+5c4+5c5
=5 + 10 + 10 + 5 + 1
=31

Is this solution Helpfull? Yes (2) | No   

RGN  (10 years ago)

When he want to call only one friend no of ways =5
when he wants to call two frnds, no of ways he can call=2+2+1=3(taking 2members at a time.if only one person is left then treat that one as a new group)
similarly

when he wants to call three frnds, no of ways he can call=3+2=2
when he wants to call four frnds, no of ways he can call=4+1=2
when he wants to call five frnds, no of ways he can call=5=1

so totally he can call one or more frnds in (5+3+2+2+1)=13 ways.

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shalvi gupta  (10 years ago)

i.31
5C1+5C2+5C3+5C4+5C5=31

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lsindhu  (10 years ago)

total no.of ways-one way in which none are invited=(2^5)-1=31

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sreeharsha  (10 years ago)

2^5-1=31

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chaitanya  (10 years ago)

ans is 31. he can invite 1 person from persons in 5 ways as he can select 1 person from 5 person in 5 ways. similarly, he can invite/select 2 persons in 5c2 ways. in that manner, ans: 5c1+5c2+5c3+5c4+5c5=31.

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ABHISHEK KUMAR  (10 years ago)

5c1+5c2+5c3+5c4+5c5=(1+1)^5-1=31

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manojgoud  (10 years ago)

among 5 friends
He want to call one friend it can be done in 5c1 ways = 5
similarly he want to call two friends in 5c2=10 , three friends in 5c3=10 ,four friends in 5c4=5 ,five friends in 5c5 ways = 1 ,so total ways are (5+10+10+5+1="31" ways ).

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SAGAR CHOWDHURY  (10 years ago)

the ans is :
5C1+5C2+5C3+5C4+5C5=31

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