Home
Class 12
MATHS
On a stormy night ten guests came to din...

On a stormy night ten guests came to dinner party and left their shoes outside the room in order to keep the carpet clean. After the dinner there was a blackout, and the guests leaving one by one, put on at random, any pair of shoes big enough for their feet, (Each pair of shoes stays together). Any guest who could not find a pair big enough spent the night there. What is the largest number of guests who might have had to spend the night there ?

Text Solution

Verified by Experts

The correct Answer is:
5
Promotional Banner

Topper's Solved these Questions

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-1 (Part-II RMO)|17 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

Similar Questions

Explore conceptually related problems

Harsha invites 13 guests to a dinner and places 8 of them at one table and remaining 5 at the other, the table being round. The number of ways he can arrange the guests is

In a dinner party, 24% of the guests are vegetarians and the rest non-vegetarians. If there are 800 guests at the dinner, the number of non-vegetarians is

20 pairs of shoes are there in a closet.Four shoe are selected at random.The probability that the yare pairs is

How many cases do you need if you have to pack 116 pairs of shoes into cases such that each hold 58 shoes?

RESONANCE-COMBINATORICS-Exercise-2 (Part-I: Previous Asked Question for Pre RMO)
  1. Consider all the 7-digit numbers containing each of the digits 1,2,3,4...

    Text Solution

    |

  2. Determine the largest 2-digit prime factor of the integer ((200),(100)...

    Text Solution

    |

  3. Find the sum of all the distinct prime divisors of underset(r=0)overse...

    Text Solution

    |

  4. Let n!, the factorial of a positive integer n, be defined as the produ...

    Text Solution

    |

  5. Find the number of ordered pairs of positive integers (a,b) such that ...

    Text Solution

    |

  6. Find the largest positive integer n such that 2^(n) divides 3^(4096)-1

    Text Solution

    |

  7. The total number of possible line segments having both end points loca...

    Text Solution

    |

  8. At a couple dance party, each man danced with exactly four women and e...

    Text Solution

    |

  9. On a stormy night ten guests came to dinner party and left their shoes...

    Text Solution

    |

  10. There are three kinds of fruits in the market. How many ways are there...

    Text Solution

    |

  11. Find the coefficient of a^(5) b^(5)c^(5)d^(8) in the expansion of the ...

    Text Solution

    |

  12. Find the total number of times the digit '2' appears in the set of int...

    Text Solution

    |

  13. Find the number of pairs of positive integers (m,n) with m le n, such ...

    Text Solution

    |

  14. How many positive integers less than 1000 have the property that the s...

    Text Solution

    |

  15. There are five cities A, B, C, D, E on a certain island. Each city is ...

    Text Solution

    |

  16. There are eight rooms on the first floor of a hotel, with four rooms o...

    Text Solution

    |

  17. Find the number of ordered triples (a,b,c) of positive integers such t...

    Text Solution

    |

  18. Suppose in the plane 10 pair wise non parallel lines intersect one ano...

    Text Solution

    |

  19. There are several tea cups in the kitchen, some with handle and the ot...

    Text Solution

    |

  20. Determine the number of 8-tuples (in(1), in(2),…, in(8)) such that in(...

    Text Solution

    |