A basket holds 30 fruits — 15 are apples, 10 are bananas, and 5 are oranges. If a person starts picking fruits from the basket one by one while blindfolded and without putting any back, what is the minimum number of fruits they must pick to be certain of getting at least one of each type?

(a) 15

(b) 16

(c) 25

(d) 26

Question

A basket holds 30 fruits &mdash; 15 are apples, 10 are bananas, and 5 are oranges. If a person starts picking fruits from the basket one by one while blindfolded and without putting any back, what is the minimum number of fruits they must pick to be certain of getting at least one of each type? 

(a) 15

(b) 16 

(c) 25

(d) 26

ONLiNE UPSC · Accepted Answer

We have a basket with 30 fruits: 15 apples, 10 bananas, and 5 oranges. 

To ensure picking at least one of each type while blindfolded and without replacement, 

We consider the worst-case scenario: 

The person could first pick all 15 apples and then all 10 bananas &mdash; that's 25 fruits without a single orange. 

Picking one more fruit (the 26th) guarantees it must be an orange, since only oranges are left. 

Thus, the minimum number of fruits needed to be picked to be sure of having at least one of each type is 26.

Hence, option d is correct.

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