Advertisements
Advertisements
प्रश्न
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
पर्याय
360
256
444
none of these.
Advertisements
उत्तर
360
The word CONSTANT consists of two vowels that are placed at the 2nd and 6th position, and six consonants.
The two vowels can be arranged at their respective places, i.e. 2nd and 6th place, in 2! ways.
The remaining 6 consonants can be arranged at their respective places in \[\frac{6!}{2!2!}\]ways.
∴ Total number of arrangements =\[2! \times \frac{6!}{2!2!}\]
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = ""^6P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
8P3
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If nP4 = 12(nP2), find n.
The possible outcomes when a coin is tossed five times:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
