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Question Number 193892 by Mastermind last updated on 22/Jun/23

$$\mathrm{Ques}.$$$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{integers}\mathrm{in}\mathrm{the}\mathrm{set}$$$$\mathrm{S}=\{1,2,3,...,60\}\mathrm{which}\mathrm{are}\mathrm{not}\mathrm{divisible}$$$$\mathrm{by}2\mathrm{nor}\mathrm{by}3\mathrm{nor}\mathrm{by}5.$$$$$$$$\mathrm{Hello}$$

Answered by BaliramKumar last updated on 22/Jun/23

$$60\times \frac{2-1}{2}\times \frac{3-1}{3}\times \frac{5-1}{5}$$$$60\times \frac{1}{2}\times \frac{2}{3}\times \frac{4}{5}=16$$$$$$

Commented by SaRahAli last updated on 22/Jun/23

$$?$$

Commented by Mastermind last updated on 22/Jun/23

$$\mathrm{Than}\mathrm{you}\mathrm{so}\mathrm{much}$$

Answered by MM42 last updated on 22/Jun/23

$$letA,B,C\subset S\mathrm{\&}A:2k;B:3k;C:5k$$$$\mid A\mid =30\mathrm{\&}\mid B\mid =20\mathrm{\&}\mid C\mid =12$$$$\mid A\cap B\mid =10\mathrm{\&}\mid A\cap C\mid =6\mathrm{\&}\mid B\cap C\mid =4\mathrm{\&}\mid A\cap B\cap C\mid =2$$$$\mid A\cup B\cup C\mid =30+20+12-10-6-4+2=44$$$$ans=60-44=16$$

Commented by Mastermind last updated on 22/Jun/23

$$\mathrm{Thank}\mathrm{you}$$

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