If the permutations of A, B, C, D, E taken al | vedclass

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

Question

(D) To find the rank of $DEBAC$,we list the letters in alphabetical order: $A, B, C, D, E$.$1$. Words starting with $A$: $4! = 24$$2$. Words starting

Vedclass · Accepted Answer

$93$

Vedclass · Answer

(D) To find the rank of $DEBAC$,we list the letters in alphabetical order: $A, B, C, D, E$.$1$. Words starting with $A$: $4! = 24$$2$. Words starting with $B$: $4! = 24$$3$. Words starting with $C$: $4! = 24$$4$. Words starting with $DA...$: $3! = 6$$5$. Words starting with $DB...$: $3! = 6$$6$. Words starting with $DC...$: $3! = 6$$7$. Words starting with $DEABC$: $1$$8$. Words starting with $DEACB$: $1$$9$. Words starting with $DEBAC$: $1$Total rank = $24 + 24 + 24 + 6 + 6 + 6 + 1 + 1 + 1 = 93$.Alternatively,using the positional method:$D$ is the $4^{th}$ letter ($3$ letters before it: $A, B, C$): $3 	imes 4! = 72$$E$ is the $4^{th}$ remaining letter ($3$ letters before it: $A, B, C$): $3 	imes 3! = 18$$B$ is the $2^{nd}$ remaining letter ($1$ letter before it: $A$): $1 	imes 2! = 2$$A$ is the $1^{st}$ remaining letter ($0$ letters before it): $0 	imes 1! = 0$$C$ is the $1^{st}$ remaining letter ($0$ letters before it): $0 	imes 0! = 0$Rank = $72 + 18 + 2 + 0 + 0 + 1 = 93$.

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

Similar Questions

The number of all $8$-digit odd numbers is

The number of ways in which all the letters of the word $COMBINATION$ can be arranged so that the vowels always come together is:

The letters of the word $ARRANGE$ are used to form different words. All these words are arranged in dictionary order. What is the rank of the word $ARRANGE$ in the dictionary?

If the best and the worst paper never appear together,then in how many ways can $6$ examination papers be arranged?

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module