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How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits?

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in Discrete Mathematics by (558k points)
How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits?

(a) 52347

(b) 50388

(c) 87658

(d) 24976

This question was posed to me in an interview.

My query is from Counting topic in division Counting of Discrete Mathematics

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Best answer
The correct choice is (b) 50388

For explanation I would say: Consider the situation as having 19 spots and filling them with 7 chocolate biscuits and 19 cheesecake biscuits. Then we just choose 7 spots for the chocolate biscuits and let the other 10 spots have cheesecake biscuits. The number of ways to do this job is ^19C7 = 50388.

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