GATE CS 2021 Set 1 Q8 — General Aptitude

To find the probability that at least two of the chosen chocolates are identical, we can use the complement rule:

Let the $10$ distinct chocolates in each bag be represented by the set $\{1, 2, \dots, 10\}$. Since one chocolate is picked from each of the $5$ bags, the total number of possible outcomes is:

Now, we calculate the number of favorable outcomes where all $5$ picked chocolates are distinct:

• The chocolate from the first bag can be any of the $10$ types.
• The chocolate from the second bag must be different from the first ($9$ choices).
• The chocolate from the third bag must be different from the first two ($8$ choices).
• The chocolate from the fourth bag must be different from the first three ($7$ choices).
• The chocolate from the fifth bag must be different from the first four ($6$ choices).

Thus, the probability that all $5$ chocolates are distinct is:

Using the complement rule:

Hence, the correct option is C.