Question

The number of ways in which one or more letters be selected from the letters $AAAABBCCCDEF$ is

• A. $476$
• B. $487$
• C. $435$
• D. $479$

Answer 1

The correct option is D $479$

The number of ways of selecting

$A=4+1=5,B=2+1=3,C=3+1=4,D=1+1=2,E=1+1=2,F=1+1=2$

So total ways of selecting is $5\times 4\times 3\times 2\times 2\times 2=480$

Above count also includes the one count when no letter is selected. we need cases when atleast one letter is selected so number of ways$=480-1=479$