3 digit number less than 200 divisible by 3 and 5
Answers
Answer:
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Step-by-step explanation:
Let A be the set of all numbers less than 250 and are divisible by 3. n(A) = (249–3)/3 + 1 =83
Let B be the set of all numbers less than 250 and are divisible by 5. n(B)=(245–5)/5 + 1=49
Let C be the set of all numbers less than 250 and are divisible by 11. n(C)=(242–11)/11 +1=22
AnB is the set of all numbers divisible by both 3 and 5. n(AnB) = no.of multiples of 15=240/15=16
BnC=set of numbers divisible by both 5 and 11
n(BnC)=220/55= 4
AnC=set of numbers divisible by both 3 and 11. n(AnC)=231/33 = 7
(AnBnC)=set of numbers divisible by 3,5 and 11 n(AnBnC )= 230/165 =2
So number of numbers divisible by 3 or 5 or 11 =n(AuBuC)=n(A)+n(B)+n(C)-n(AnB)-n(BnC) -n(AnC) + n(AnBnC) = 83+49+22–16–4–7+2=129