abeer16 wrote:

a student is to answer 7 out of 10 questions in an examination .how many choices has she.how many if she must answer at least 3 of the first 5 questions

Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html Make sure you type the question in exactly as it was stated from the source.

Provide answer choices for PS questions.As for your question, I guess question means that student must answer exactly 7 questions.

A student is to answer 7 out of 10 questions in an examination.

1. How many choices has she? Choosing different 7 questions to answer out of 10 -

C^7_{10}=\frac{10!}{7!3!}=120;

2. How many if she must answer at least 3 of the first 5 questions? At least 3 out of firts 5 means 3, 4, or 5 out of first 5 questions (so 4, 3, and 2 question out of next 5):

C^3_5*C^4_5+C^4_5*C^3_5+C^5_5*C^2_5=50+50+10=110.

Hope it's clear.

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