Class 11

Math

Algebra

Permutations and Combinations

How many words can be formed with the letters of the word $_{′}PATALIPUTRA_{′}$ without changing the relative order of the vowels and constants?

- $3600$
- $3800$
- $3200$
- $4800$

we have 6 consonants $⇒PTLPTR$

and 5 vowels$⇒AAIUA$

letter P takes $_{6}C_{2}$ places

T takes $_{4}C_{2}$ places out of remaining 4 places

L takes $_{2}C_{1}$ places out of remaining 2 places

R takes $1$ remaining place

Similarly,

Letter A takes $_{5}C_{3}$ places

I takes $_{2}C_{1}$ places out of remaining 2 place

U takes 1 remaining place

$∴$Total number of ways

$=3600$ ways

Hence, option 'A' is correct.