Permutation and combination

There are 5 bottles of sheery and each has their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the correct bottle?

I think the answer is 24

I think the answer is 24

__________________

n/a

total no. of ways of

total no. of ways of applying caps to bottle...

5*5*5*5*5 = 3125.

Now no. of ways in which 1 cap is on d correct bottle = 5

no. of ways in which 2 cap is on d correct bottle = 5C2 = 10

no. of ways in which 3 cap is on d correct bottle = 5C3 = 10

no. of ways in which 4 cap is on d correct bottle = 5C4 = 5

no. of ways in which 5 cap is on d correct bottle = 1

so in all 21.

so no. of ways so that not a single cap is on the correct bottle are
= 3125 - 21
= 3104

Solution to problem

Here consider each cap is different the all posible combination = 5! =5x4x3x2 =120

If one cap is correct then ways = 4! = 24

If two are correct then ways = 3! = 6

If three are correct then ways = 2! = 2

If four are correct then ways = 1 ways and fifth is also on the correct bottle thus answer should be

120-24-9 = 87

solution 2 problem

its 5*5*5*5*5= 2525 ways

but since only one way is correct so it will be 2525-1= 2524 ways.

solution 2 problem

it will be 5*5*5*5*5= 3125ways
only one way is correct so subtract dat one
so 3125-1= 3124 ways

shaheen is correct

shaheen is correct

HUMRAJ!!!!!

No body is found right answer.

 plz try once again..........

is 45 the answer?

is 45 the answer?

CORRECT Answer :

According to me the answer of above Question should be : 32......... can some one plz verify ???

i found out the mistake....

total no. of ways of applying caps to bottle...

5*5*5*5*5 = 3125.

Now no. of ways in which 1 cap is on d correct bottle = 5*4! = 120

no. of ways in which 2 cap is on d correct bottle = 5C2 * 3! = 10*3! = 60

no. of ways in which 3 cap is on d correct bottle = 5C3 *2! = 10*2! = 20

no. of ways in which 5 cap is on d correct bottle = 1

so in all 201.

so no. of ways so that not a single cap is on the correct bottle are
= 3125 - 201
= 2924

plz let me know is it correct or not?

regards,
shaheen

Post new comment

  • Web page addresses and e-mail addresses turn into links automatically.
  • Allowed HTML tags: <a> <em> <strong> <small> <sup> <sub> <cite> <blockquote> <code> <ul> <ol> <li> <dl> <dt> <dd> <h1> <h2> <h3> <h4> <h5> <h6> <font> <img> <br> <br /> <p> <div> <span> <b> <i> <u>
  • Lines and paragraphs break automatically.

More information about formatting options