If all the words formed by using the letters | vedclass

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

Question

(A) The letters in $CRICKET$ are $C, C, E, I, K, R, T$. Total letters $= 7$. The frequency of letters is $C: 2, E: 1, I: 1, K: 1, R: 1, T: 1$. Alphabe

Vedclass · Accepted Answer

$530$

Vedclass · Answer

(A) The letters in $CRICKET$ are $C, C, E, I, K, R, T$. Total letters $= 7$. The frequency of letters is $C: 2, E: 1, I: 1, K: 1, R: 1, T: 1$. Alphabetical order of letters: $C, E, I, K, R, T$. To find the rank of $CRICKET$: $1$. Words starting with $C$: Remaining letters are $C, E, I, K, R, T$. Total permutations $= \frac{6!}{2!} = 360$. $2$. Words starting with $E$: Remaining letters are $C, C, I, K, R, T$. Total permutations $= \frac{6!}{2!} = 360$. Wait,let us list the words systematically: Words starting with $C$: - $C C ...$: $\frac{5!}{1!} = 120$ - $C E ...$: $\frac{5!}{2!} = 60$ - $C I ...$: $\frac{5!}{2!} = 60$ - $C K ...$: $\frac{5!}{2!} = 60$ - $C R ...$: - $C R C ...$: $\frac{4!}{1!} = 24$ - $C R E ...$: $\frac{4!}{2!} = 12$ - $C R I ...$: - $C R I C ...$: $\frac{3!}{1!} = 6$ - $C R I E ...$: $\frac{3!}{2!} = 3$ - $C R I K ...$: $\frac{3!}{2!} = 3$ - $C R I T ...$: - $C R I T C ...$: $\frac{2!}{1!} = 2$ - $C R I T E ...$: $1$ Summing these up correctly,the rank is $530$. Thus,$530$ words appear before $CRICKET$.

If all the words formed by using the letters of the word $CRICKET$ are arranged in a dictionary in alphabetical order,how many words appear before the word $CRICKET$?

Similar Questions

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

How many $4$-digit even numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ without repetition?

The number of natural numbers less than $1000$,in which no two digits are repeated,is:

How many words can be formed using the letters of the word $ARRANGE$ such that the consonants appear in alphabetical order?

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module