Question

How many different words can be formed with the letters of the word HARYANA ? How many of these

(i) Have H & N together? (Ans. 120) (ii) Begin with H and end with N? (Ans. 20)

(iii) Have three vowels together? (Ans. 120)

Answer 1

Answer:

Step-by-step explanation:

HARYANA

H   R    N    Y    A-Thrice

(i) Have H & N together

Taking HN as 1 block   we Have now total 6 letter

= 6!  * 2 ! / 3!    (  H& N can be arranged in 2!  ways  & A is thrice so divided by 3!)

= 6 * 5 * 4 / 2

= 60

if HN  sequence is defined then 120

(ii) Begin with H and end with N

We Left with total 5  where A is repeated thrice

= 5!/3!

= 5 * 4

= 20

(iii) Have three vowels together

Taking AAA as 1 block we have now total 5 letter

= 5!  

= 120

Answer 2

Answer:120

Step-by-step explanation:HRYN(AAA)

5!×{3!÷3!}

=5!=120