The number of words formed with letters PATALIPUTRA without changing the order of vowel & consonants..????

Hello student,

we need to arrange - C=consonant, V=Vowel
CVCVCVCVCCV
For V's we have to CHOOSE where to put the A's (as they are all the same - we simply choose 3 locations out of the 5 for the A's).That is 5C3.then we have two options to place the I and the U must be in the last available place.
Total number of arrangements for V's - 5C3x2x1 = 10x2x1 = 20.
C's -we CHOOSE the two locations for the P's 6C2 and then two locations for the T's 4C2 and then place the L in one of two places and the R lands in the last available place.
number of arrangements for C's - 6C2 x 4C2 x2x1 = 15x6x2x1 = 180
total words = 180x20 = 3600.

Thanks and Regards

Shaik Aasif

askIITians faculty

Let us arrange it as cvcvcvcvccv . We can arrange vowels through 5!÷3! And we can arrange consonants through 6!÷2!2! . Then by principle of multiplication required no. Of ways = (5!÷3!) ×(6!÷2!2!)