The number of 4 letter words that can be formed from the letters of the word ALLAHABAD are 
 

In the word ALLAHABAD there are $AAAA,LL,H,B,D$

Number of 4 letter words with all different letters A,L,H,B,D=${ }^5{P}_4=120$

Number of 4 letter words with 2 identical and 2 different= $2{\times }^4{C}_2\times \frac{4!}{2!}=144$

Number of 4 letter words with 2 pairs of identical letters=$\frac{4!}{2!2!}=6$

Number of 4 letter words with 3 identical letters and one different=${ }^4{C}_1\times \frac{4!}{3!}=16$

Number of 4 letter words with 4 identical letters=1

Total=120+144+6+16+1=287