Question #81855

Total no. Of outcomes= 6*4
= 24
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alternate derivation:
There are 4 choice for the first digit;
for each of these there are 3 choices for the second digit;
for each of these there are 2 choices for the third digit;
leaving only 1 possibility for the fourth digit.
Total number of ways of composing a 4-digit number #=4xx3xx2xx1=24#
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Outcomes where divisibility by 5 is possible = 6
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explanation of derivation:
To be divisible by 5 the last digit must be 5;
this leaves 3 choices for the first digit;
2 choices for the second digit; and
1 possibility left for the last digit.
Number of ways of composing 4-digit number ending in 5: #=3xx2xx1=6#
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Hence probability of getting a no. which is divisible by 5 = 6/24 = 1/4
Probability =1/4

The probability can be calculated by dividing the number of outcomes fulfilling the condition by the total number of outcomes:

#P(A)=(bar(bar(A)))/bar(bar(Omega))#

Here the number of all outcomes can be calculated as:

#bar(bar(Omega))=4! =24#

The condition for outcomes in #A# is: the number is divisible by 5, so its last digit has to be #5# (a number is divisible by #5# if its units digit is #0# or #5#, but #0# is not in the set).
The remaining 3 digits can be arranges in #3! = 6# ways, so:

#bar(bar(A))=3! =6#

Now we can calculate the probability:

#P(A)=4/24=1/4=0.25#

Original answer:

Probability = Favorable outcome / Total outcome

Outcomes= 1253 1235 1523 1532 1352 1325 2135 2153 2351 2315 2513 2531 3512 3521 3125 3215 3152 3251

Total number of outcomes= 18

Favorable outcomes=1235 1325 2135 2315 3125 3215

Number of favorable outcome= 6

Probability= Favorable outcome / Total outcome

              =  #6/18#
              = 3