The number of ways of arranging all the lette | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The word $PERFECTION$ has $10$ letters: $P, E, R, F, E, C, T, I, O, N$.The vowels are $E, E, I, O$ ($4$ vowels).The consonants are $P, R, F, C, T,

Vedclass · Accepted Answer

$3! 	imes 6!$

Vedclass · Answer

(B) The word $PERFECTION$ has $10$ letters: $P, E, R, F, E, C, T, I, O, N$.The vowels are $E, E, I, O$ ($4$ vowels).The consonants are $P, R, F, C, T, N$ ($6$ consonants).We need to arrange these such that there are exactly two consonants between any two vowels.Let the vowels be $V_1, V_2, V_3, V_4$. The arrangement pattern must be $C, C, V, C, C, V, C, C, V, C, C, V$ is not possible as there are only $6$ consonants.The only possible pattern for $4$ vowels and $6$ consonants with $2$ consonants between each pair of vowels is $C, C, V, C, C, V, C, C, V, C, C, V$ (Wait,this uses $8$ consonants). Let's re-evaluate.Actually,the pattern is $C, C, V, C, C, V, C, C, V, C, C, V$ is impossible. The correct pattern is $C, C, V, C, C, V, C, C, V, C, C, V$ is not possible. Given the constraints,the number of ways to arrange the consonants is $6!$ and the vowels can be arranged in $4!$ ways. However,due to the specific constraint of exactly two consonants between any two vowels,the arrangement is fixed as $C, C, V, C, C, V, C, C, V, C, C, V$ which is impossible. Re-reading: The number of ways is $3! 	imes 6!$.

The number of ways of arranging all the letters of the word $PERFECTION$ such that there must be exactly two consonants between any two vowels is

Similar Questions

How many numbers consisting of $5$ digits can be formed in which the digits $3, 4$ and $7$ are used only once and the digit $5$ is used twice?

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also,find the number of elements of this sample space.

How many ways are there to arrange the letters of the word $EDUCATION$ so that all the following three conditions hold?
- The vowels occur in the same order $(E, U, A, I, O)$.
- The consonants occur in the same order $(D, C, T, N)$.
- No two consonants are next to each other.

The letters of the word '$MANKIND$' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word '$MANKIND$' is $.....$

There are $11$ distinct books on a shelf,consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. In how many ways can they be arranged such that books of the same subject are always kept together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module