Question

1. I am a 10 letter word starting with P and ending
with 'Y'. I contain three vowels and is studied to
learn about the meaning of life and reality. Those
who are deeply versed in me are considered very
wise.​

Answer 1

Answer:

(i) Given word is PERMUTATIONS

Now we have to find no. of ways we can arrange the letters with starting P and end with S

Total letters =10 in wj=hich we have 2T

′

s,

if P and S are fixed

then no. of arrangement =

2!

10!

=181440

(ii) vowels in given word are : AEIOU

considering vowels as one string

Then

AEIOU

PRMTTNC

can be arrange in

2

−8

×5!=2419200

(iii) we have to select 4 letters between P and S and their are 10 letters

Therefore No. of ways =

10

C

2

=210

and , P and S can also change their position

∴ No of ways =420 [Double of 210]

Now 4 letters can arrange in 4! ways

Now no of ways four letters arrange between P and S are 4!×420=10080

Now consider

P 4 S

as one string

Now remaining 6 letters +one string can

be arrange in 7! ways

Total no. of ways =10080×7!/2

=

2

50,803,200

=25401600