5 letters be put into 3 letter boxes A,B,C...
// means 5 different letters in 3 different boxes..
condition : letter box A contains at least 2 letters...
method 1:
required ways where letter box A has at least 2 letters= box A has 2 letters + box A has #letters + box A has 4 letters + box A has 5 letters
=5C2*2^3 + 5C3*2^2+5C4*2^1 +5C5
=80+40+10+1 =131 answer...
shortcut method:
required ways where letter box A has atleast 2 letters=total ways - at most one letter in box A
= total number of ways in which each letter can be assigned to any letter box - when letter box A has 1 letter - letter box A has no letter.
=> 3^5 - 5C1*2^4 - 5C0*2^5
=243- 5*16 - 32
=243-112 = 131 answer....