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A lady gives a dinner party to 5 guests ...

A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together, is

A

56

B

126

C

91

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C

`.^(9)C_(5)-.^(9-2)C_(5-2)=.^(9)C_(4)-.^(7)C_(3)`
`=126-35=91`
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Single Option Correct Type Questions)
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  2. If a,b,c and d are odd natural numbers such that a+b+c+d=20, the numbe...

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  3. If l=LCM of 8!, 10! and 12! and h = HCF of of 8!, 10! and 12! then l/h...

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  4. The number of positive integers satisfying the inequality C(n+1,n-2)-C...

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  5. The number of ways in which a score of 11 can be made from a throw by ...

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  6. The number of positive integers with the property that they cann be ex...

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  7. In a plane there are 37 straight lines, of which 13 pass pass through ...

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  8. If a denotes the number of permutations of (x+2) things taken all at a...

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  9. The number of numbers less than 1000 than can be formed out of the dig...

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  10. If the permutations of a, b, c, d, e taken all together be written dow...

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  11. On a railway there are 20 stations. The number of different tickets re...

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  13. The straight lines I(1),I(2),I(3) are paralled and lie in the same pla...

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  14. Let A be a set of n (>=3) distinct elements. The number of triplets (x...

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  15. The total number of five-digit numbers of different digits in which...

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  16. The total number of words that can be formed using all letters of the ...

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  17. A man has three friends. The number of ways he can invite one frien...

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  18. The number of three digit numbers of the form xyz such that x lt y , z...

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  19. The letters of the word 'MEERUT' are arranged in all possible ways as ...

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  20. The number of ways in which 10 condidates A(1),A(2),......,A(10) can b...

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