I wasn't sure what the question meant at first - it sounded to me as if we were making ice cream cones each with three scoops of different flavored ice cream. I don't think that's what the question means though -- I think it's asking how many ways we could choose 4 one-scoop ice cream cones, if we'll only be choosing from three of the six available flavours. Now, assuming we're choosing exactly three flavours (not two or one), then we must be choosing two identical cones, and then two cones of other flavours. We have 6 choices for the two identical cones, and then 5C2 = 10 choices for the remaining two, for 60 choices in total.

Alternatively, you can pick the three different cones first, in 6C3 = 20 ways, and then choose which of those 3 to duplicate, for 20*3 = 60 choices.

That's if I'm interpreting the question correctly, which I'm unsure of - the wording could be improved.
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We have 6 flavors and 4 ice cream cones. We have to choose 3 different flavors for these 4 cones.

For the first 3 cones we choose any 3 flavors in 6C3 = 6 * 5 * 4/ 3 * 2 = 20 ways

For the 4th cone, we choose one of the 3 selected flavors in 3C1 = 3 ways

Total number of ways = 20 * 3 = 60


Option B

Arun Kumar
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