Gate CS 2025 (CS1)| Question - 10 | General Aptitude

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential.
If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

Solution:

Here $x_{1} x_{2} x_{3} x_{4}$ flavor
$x ₁ + x ₂ + x ₃ + x ₄ = 3 s q u a r e x ₁ + x ₂ + . . . + x ᵣ = n [n o n - n e g a t i v e i n t e g e r s o l u t i o n s] \Rightarrow {(n + r - 1)}_{C (r - 1)} \Rightarrow {(3 + 4 - 1)}_{C (4 - 1)} \Rightarrow ⁶ C ₃ = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$

Gate CS 2025 (CS1)| Question - 10 | General Aptitude

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