Advertisements
Advertisements
Question
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
Solution
In order to find the number of even digits, we fix the unit's digit as an even digit.
Fixing the unit's digit as 2:
Number of arrangements possible = 6P2 = `6xx5=30`
Similarly, fixing the unit's digit as 4:
Number of arrangements possible = 6P2 = `6xx5=30`
Fixing the unit's digit as 6:
Number of arrangements possible = 6P2 =`6xx5=30`
∴ Number of 3-digit even numbers that can be formed = 30 + 30 + 30 = 90
APPEARS IN
RELATED QUESTIONS
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 3)! = 56 [(n + 1)!], find n.
If nP4 = 360, find the value of n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
In how many ways can five children stand in a queue?
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
How many three-digit numbers are there, with distinct digits, with each digit odd?
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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 = 182 bc, find the value of x.
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?
All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letter G always occupies the first place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?
Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
