1)If I roll to three tetrahedral dice (dice with only four faces), assume that t
ID: 3005948 • Letter: 1
Question
1)If I roll to three tetrahedral dice (dice with only four faces), assume that the digits on two of the dice are 1, 2, 3 and 4 and the third die has the digit 3,5,6 and 7 on it.
a)How many different combinations of the dice are possible (1 on the first die and 2 on the second die and 7 on the third die is considered a different combination than 2 on the first die and 1 on the second die and 7 on the third die).
b)What is the lowest possible sum on the three dice? (Show a combination that will produce this lowest value)
c)What is the largest possible sum on the three dice? (Show a combination that will produce this highest value)
d) In how many different ways can a sum of 11 be obtained? (list them all)
e)In how many ways can the sum of 6 be obtained? (list them)
Explanation / Answer
a)
4 numbers on first dice,4 on second and 4 on third. Each is independent of the other.
So total combinations are:4*4*4=64
b)
Since each dice is independent so lowest sum is obtained when lowest number is obtained on each dice.
Hence lowest sum is : 1+1+3=5
c)
Since each dice is independent so largest sum is obtained when largest number is obtained on each dice.
Hence largest sum is: 4+4+7=15
d)
Case 1: Number on third dice is: 3
Hence sum on first two die must be:8
This can happen in only 1 way with 4 on each
Case 2: Number on third dice is: 5
Hence sum on first two die must be: 6
This can happen in 3 ways: 2 on first dice,4 on second or 4 on first dice and 2 on second or 3 on both dice
Case 3: Number on third dice is: 6
Hence sum on first two die must be: 5
This can happen in 4 ways: 2 on first dice,3 on second or 3 on first dice and 2 on second
1 on first dice, 4 on second or 4 on first dice or 1 on second.
Case 4: Number on third dice is: 7
Hence sum on first two die must be: 4
This can happen in 3 ways: 1 on first dice,3 on second or 3 on first dice and 1 on second or 2 on both
Hence 11 sum can be obtained in: 1+3+4+3=11 ways
e)
Case 1: 3 on third dice
Hence a sum of 3 on first two die. This is done in two ways:
1 on first die and 2 on second or 2 on first die and 1 on second dice.
Case 2: 5,6,7 on third dice
Hence a sum 1 or less on first two die.
This is not possible.
Hence sum of 6 is obtained in 2 ways
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