Question

Q3. Suppose a language containing five letters: A, B, C, D, E (5%) (b) How many four-letter words can you form if each letter appears only once in each word? (5%) (c) What is the probability that a three-letter word (with each letter appearing only once) con (a) How many three-letter words can you form in this language? tains E? (5%)

Answer 1

a)

as for each letter; there are 5 options; therefore number of three letter words=5*5*5=125

b)

as for first letter we have 5 choices ; for second letter 4 choices except that which is selected for first; for third letter 3 choice and for 4th 2 choices

hence for 4 letter words =5*4*3*2=120

c)

number of ways to select 3 letter word (without replacement)=5*4*3=60

number of ways to select 3 letter word without having E =4*3*2=24

hence number of ways to select 3 letter word having E =60-24=36

therefore probability =36/60=0.6