If 4 dice are rolled what are the different combinations possible
Answers
Answer: the answer is : 671
Step-by-step explanation:
Two examples given in class:
1) If we roll four dice, what is the probability of at least one six?
a) Consider the complement problem, there is a 5/6 probability of not rolling a six
for any given die, and since the four dice are independent, the probability of not rolling a
six is (5/6)4 = 54
/6
4 = 625/1296. The probability of rolling at least one six is therefore
1 − 625/1296 = 671/1296 ≈ .517.
b) Alternatively, recall that the number of ways of choosing r objects from a collection
of N is N
r
= N!/r!(N − r)! .
Any of the four dice can be the one that comes up six, and the other three don’t, so
the number of ways that exactly one of the four dice is six is
4
1
· 5
3 = 4 · 5
3 = 500
exactly two sixes:
4
2
· 5
2 = (4 · 3/2) · 5
2 = 150
exactly three sixes:
4
3
· 5 = 4 · 5 = 20
exactly four sixes:
4
4
= 1
The total number of possibilities is 500 + 150 + 20 + 1 = 671, and hence the probability is
671/6
4
, in agreement with the ab
When four dice are rolled simultaneously,there will be a total of 6×6×6×6=1296 outcomes.the number of outcomes in which none of the four dice show 3 will be 5×5×5×5=625outcomes.
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