Binomial Probability Distribution Bernoulli Trials Lesson by Anil Kumar to Amy GCSE Level A

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Hi Sir,
Can you please provide assistance in solving this question:

(a) Pigeonhole Principle: Fifty points lie in a 10mm cube. Prove that seven of these points lie in a 5mm cube.

b)This question using the inclusion-exclusion principle: A childcare centre has 40 children registered, of whom 19 are boys. The
centre specialises in arts and craft, with 10 girls and 7 boys having at least one parent
who is a professional artist and 8 boys and 8 girls with at least one parent who is
a professional craftsperson. There are 7 boys and 5 girls with parents from neither
profession. Of the 5 children with parents from both, how many are boys?

Thank you

samuelraj