Question

How many different words can be formed out of the letters of the word MORADABAD taken four at a time?

Answer 1

We have thirteen letters.
$2l,3N,2T,2A$ and $(E,O,L,R)8$ (types)
We can select 5(five) letters in the following manner:
1. All different ${{}^{8}C}_5=\frac{\mathrm{8.7.5}}{\mathrm{1.2.3}}=56$ ways
2. 2 alike, 3 different ${{}^{4}C}_1.{{}^{7}C}_3=435=140$ ways (we have 4 sets of alike letters)
3. 3 alike, 2 different ${{}^{1}C}_1.{{}^{7}C}_2=1.21=21$ ways (we have only one set of 3 alike)
4. 3 alike and 2 alike ${{}^{1}C}_1.{{}^{3}C}_1=1.3=3$ ways
5.Two sets of alike and one different
${{}^{4}C}_2.{{}^{6}C}_1=6.6=36$ ways
$\therefore$ Total number of selection is
$56+140+21+3+36=256$ ways $⟹$ (d)