Computer Information Systems

To solve this problem, we need to determine the number of ways to choose 20 cupcakes from 8 different kinds with the constraints that at most 3 can be red velvet and at least 4 must be strawberry. First, let's denote the different kinds of cupcakes as follows: A A - Red velvet B B - Strawberry C , D , E , F , G , H C, D, E, F, G, H - Other flavors We aim to find the number of ways to select 20 cupcakes such that: The number of red velvet cupcakes, x A x_A , is at most 3 ( 0 ≤ x A ≤ 3 0 \leq x_A \leq 3 ). The number of strawberry cupcakes, x B x_B , is at least 4 ( x B ≥ 4 x_B \geq 4 ). The total number of cupcakes is 20 ( x A + x B + x C + x D + x E + x F + x G + x H = 20 x_A + x_B + x_C + x_D + x_E + x_F + x_G + x_H = 20 ). Let's split the problem into cases based on the number of red velvet cupcakes x A x_A . Case 1: x A = 0 x_A = 0 We need to select 20 cupcakes with x B ≥ 4 x_B \geq 4 x . Let y B = x B − 4 y_B = x_B - 4 (i.e., <sema

Computer science

There are eight different kinds of cupcakes available in a bakery. Each kind is in abundant supply there.

How many options are there to choose 20 cupcakes if at most 3 can be red velvet and at least 4 must be strawberry?

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Computer science

Computer science

Manu

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