Consider the alphabet ABCDEF a How many four letter words co

Consider the alphabet A,B,C,D,E,F.

a. How many four letter words contain the subword ACE?

b. How many four letter words don\'t begin with F or don\'t end in E?

c. How many five letter words contain the subword CAB?

d. How many four letter words begin with C or end in two vowels?

Solution

a) total 6 letters are there

as in 4 letter word is we fix 3 letter subword ace then we will left with 6 option only

now these 6 letter can be prefix or suffix in ace

therefore there will be 6+6 = 12 words

b)if we dont consider the repetition of letters then

at first place 5 letters can come , 2nd place 5 letters can come, 3rd place 4 letters can come, 4th place 3 letters can come.

so total options are 5*5*4*3= 600

c)subword CAB

SO 6 LETTERS CAN COME AT TWO PLACE 1ST TWO AND ALSO 6 LETERS CAN COME ON 4TH AND 5TH POSTITION

SO TOTAL WORDS = 6+6+6+6= 24

D)IF WE DONT CONSIDER THE REPETITION OF LETTER

THEN ON LAST 2 POSITION EITHER A OR E CAN COME

1ST POSITION C IS THERE

WE LEFT WITH 2ND POSITION WHERE 3 CAN COME B,D,F

SO TOTAL WILL BE 3+1+1=5