Six digits are chosen randomly from the set {0,1,2,…,9} a.) what is the probability that all six digits are the same? b.) what is the probability that five or more of the digits of the same?

a) 0.00001

b) 0.001

Step-by-step explanation:

Given numbers,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

a) If by these numbers we have to make six digit number,

So, the total ways of arranging 6 digit number =

Now, if all six digit in the number are same,

Then the possible ways = 10   ( eg : 000000, 111111, 222222, 333333, 444444... etc ),

Hence, the probability that all six digits are the same

b) The ways that five or more of the digits of the same = exactly 5 digits are same + Exactly 6 digits are same

∵ The ways that 5 digits are same = 10 × 9 = 90 (i.e. 111110, 111112, 111113,.....9 times, 222220, 222221,.....9 times .... etc..)

So, the number of ways that 5 or more than 5 digits are same = 90 + 10 = 100

Hence, the probability that five or more of the digits of the same