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The given digits are:-

0,1,2,3,4,5

Now since we know that no two digit number can start with 0 hence we will first list all the numbers starting with 1:

10, 11, 12,13,14,15

Now, we will list all the numbers starting with 2:-

20, 21, 22,23,24,25

Now, we will list all the numbers starting with 3:-

30, 31, 32,33,34,35

Now, we will list all the numbers starting with 4:-

40, 41, 42,43,44,45

Now, we will list all the numbers starting with 5:-

50, 51, 52,53,54,55

Therefore the sample space S is given by:-

\[S = \left\{ {10,{\text{ }}11,{\text{ }}12,13,14,15,20,{\text{ }}21,{\text{ }}22,23,24,25,30,{\text{ }}31,{\text{ }}32,33,34,35,40,{\text{ }}41,{\text{ }}42,43,44,45,50,{\text{ }}51,{\text{ }}52,53,54,55} \right\}\]

Now counting the number of elements in S we get:-

\[n\left( S \right) = 25\]

Now since we know that a number is divisible by 5 if its unit’s place contains 0 or 5.

Hence listing such numbers from S which have 0 or 5 at unit’s place we get:-

10,15,20,25,30,35,35,40,45,50,55

Since the U is the event that it contains the number which is divisible by 5

Hence, U is given by:-

\[U = \left\{ {10,15,20,25,30,35,35,40,45,50,55} \right\}\]

Now counting the number of elements in U we get:-

\[n\left( U \right) = 11\]

Therefore,

Sample space S is:

\[S = \left\{ {10,{\text{ }}11,{\text{ }}12,13,14,15,20,{\text{ }}21,{\text{ }}22,23,24,25,30,{\text{ }}31,{\text{ }}32,33,34,35,40,{\text{ }}41,{\text{ }}42,43,44,45,50,{\text{ }}51,{\text{ }}52,53,54,55} \right\}\]

Number of elements in S are:-

\[n\left( S \right) = 25\]

The event U is:-

\[U = \left\{ {10,15,20,25,30,35,35,40,45,50,55} \right\}\]

Number of elements in U are:-

\[n\left( U \right) = 11\].