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?
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
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
its 5*5*5*5*5= 2525 ways
but since only one way is correct so it will be 2525-1= 2524 ways.
it will be 5*5*5*5*5= 3125ways
only one way is correct so subtract dat one
so 3125-1= 3124 ways
No body is found right answer.
plz try once again..........
According to me the answer of above Question should be : 32......... can some one plz verify ???
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
I think the answer is 24
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