Question

How many three digit numbers have at least one 2 and at least one 3 is

• A. 52
• B. 48
• C. 54
• D. 46

Answer 1

Answer: (A)

Let 'U' be the set of all three digit numbers Let 'S' be the set of all three digit numbers not containing '2'.
Let 'T' be the set of all three digit numbers not containing '3'.
$n(U)=999-99=900$
$n(S)=8\times 9^2=648$
$n(T)=8\times 9^2=648$
$n(S\cap T)=7\times 8^2=448$
$n\left(S\cup T\right)=n\left(S\right)+n\left(T\right)-n\left(S\cap T\right)$
$-648+648-448=848$
$n\left[U-\left(S\cup T\right)\right]=n\left(U\right)-n\left(S\cup T\right)$
$=900-848=52$