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  • Question
  • A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?


  • Options
  • A. 3
  • B. 5
  • C. 3!
  • D. 5!

  • Correct Answer


  • Explanation

    The possible outcomes that satisfy the condition of "at least one house gets the wrong package" are:
    One house gets the wrong package or two houses get the wrong package or three houses get the wrong package.

    We can calculate each of these cases and then add them together, or approach this problem from a different angle.
    The only case which is left out of the condition is the case where no wrong packages are delivered.

    If we determine the total number of ways the three packages can be delivered and then subtract the one case from it, the remainder will be the three cases above.

    There is only one way for no wrong packages delivered to occur. This is the same as everyone gets the right package.

    The first person must get the correct package and the second person must get the correct package and the third person must get the correct package.
     1󪻑=1

    Determine the total number of ways the three packages can be delivered.
     3󫎽=6

    The number of ways at least one house gets the wrong package is:
      6?1=5
    Therefore there are 5 ways for at least one house to get the wrong package.


  • More questions

    • 1. 
      If a : b = 2 : 3 and 2 : a =1 : 2, then the value of 'b' is?

    • Options
    • A. 4
    • B. 6
    • C. 1 / 3
    • D. 3 / 2
    • Discuss
    • 2. 
      0.6 of a number equals 0.09 of another number. The ratio of the number is?

    • Options
    • A. 2 : 3
    • B. 1 : 15
    • C. 20 : 3
    • D. 3 : 20
    • Discuss
    • 3. 
      If a/3 = b/8, then ( a + 3 ) : ( b + 8 ) is equal to?

    • Options
    • A. 3 : 8
    • B. 8 : 3
    • C. 5 : 8
    • D. 3 : 5
    • Discuss
    • 4. 
      4, 19, 49,?, 229

    • Options
    • A. 75
    • B. 109
    • C. 65
    • D. 169
    • Discuss
    • 5. 
      777777 / 11 =?

    • Options
    • A. 7077
    • B. 70707
    • C. 7707
    • D. 7007
    • Discuss
    • 6. 
      Find the cardinal number of the following set {x: x is a natural number ? 30 and is divisible by 7 or 11}

    • Options
    • A. 4
    • B. 8
    • C. 6
    • D. 2
    • Discuss
    • 7. 
      SBI lent ? 1331 lakh to the TATA group at compound interest and got ?1728 lakh after 3 yr. What is the rate of interest charged, if compounded annually?

    • Options
    • A. 11%
    • B. 9.09%
    • C. 12%
    • D. 8.33%
    • Discuss
    • 8. 
      The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the two numbers.

    • Options
    • A. 1
    • B. 3/5
    • C. 1/2
    • D. 11//6
    • Discuss
    • 9. 
      5 men and 6 women can earn ? 2160 in 4 days. 8 men and 10 women can earn ? 4400 in 5 days. In how many days can 4 men and 9 women earn ? 1800?

    • Options
    • A. 3
    • B. 4
    • C. 5
    • D. 6
    • Discuss
    • 10. 
      A train 110 metres long travels at 60 km/hr. How long does it take to cross a telegraph post?

    • Options
    • A. 5 sec.
    • B. 5.6 sec
    • C. 6.6 sec
    • D. 6.8 sec
    • Discuss


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