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[pemdas]

In how many ways four fair dices, which are numbered and tossed simultaneously, have different numbers?

[rijul007]

In how many ways four fair dices, which are numbered and tossed simultaneously, have different numbers?

1st dice - can have 6 possible values
2nd dice- can have 5
3rd dice- 4
4th dice-3

So total no would be = 6*5*4*3 = 360


Or u can also think it this way-
Select 4 different nos between 1 and 6 inclusive and arrange them amongst themselves = 6P4

[pemdas]

and..

[rijul007]

and..

The ans is 360

[rijul007]

reply to the pm:
the dices were numbered remember
4,6,2,1 is not the same as 1,6,4,2

[pemdas]

remember they tossed simultaneously
so, it's actually overcounting the number of ways by 4!

reply to the pm:
the dices were numbered remember
4,6,2,1 is not the same as 1,6,4,2

[rijul007]

the dices were tossed simultaneously... True
But its also mentioned that the dices are numbered.. Making each one of them unique...

[pemdas]

who says dices are unique - they are numbered 1-6
the dices are tossed at once, if you have 1-2-3-4 and 2-3-4-1 what is the difference between these two sets. Both contain the four dices with the same numbers

BTW, i made this up to puzzle and solved for 15= 6C4 or 6P4/4!

the dices were tossed simultaneously... True
But its also mentioned that the dices are numbered.. Making each one of them unique...

[user123321]

who says dices are unique - they are numbered 1-6
the dices are tossed at once, if you have 1-2-3-4 and 2-3-4-1 what is the difference between these two sets. Both contain the four dices with the same numbers

BTW, i made this up to puzzle and solved for 15= 6C4 or 6P4/4!

the dices were tossed simultaneously... True
But its also mentioned that the dices are numbered.. Making each one of them unique...

I thought 6P4 too
Nice trap. Need to be double extra careful while solving simple questions

user123321