Q. 24.0( 125 Votes )

# How many 4-digit numbers are there with no digit repeated?

Answer :

In questions like these we need to fill the places that are to be occupied.**To find:** Four digit number (digits does not repeat)

Now we will have 4 places where 4 digits are to be put.

So,

At thousand's place = There are 9 ways as 0 cannot be at thousand's place = 9 ways

At hundredth's place = There are 9 digits to be filled as 1 digit is already taken = 9 ways

At ten's place = There are now 8 digits to be filled as 2 digits are already taken = 8 ways

At unit's place = There are 7 digits that can be filled = 7 ways

Total Number of ways to fill the four places = 9 × 9 × 8 × 7 = 4536 ways.

So a total of 4536 four digit numbers can be there with no digits repeated.

Rate this question :

Which of the following are true :

(2 + 3)! = 2! + 3!

RD Sharma - MathematicsHow many A.P.’s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?

RD Sharma - MathematicsFour 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?

RD Sharma - MathematicsHow many permutations can be formed by the letters of the word, ‘VOWELS,’ when

all vowels come together?

RD Sharma - MathematicsFind the total number of ways in which six ‘+’ and four ‘-‘ signs can be arranged in a line such that no two ‘-‘ signs occur together.

RD Sharma - MathematicsIn how many ways can the letters of the word “INTERMEDIATE” be arranged so that :

i. the vowels always occupy even places?

ii. the relative order of vowels and consonants do not alter?

RD Sharma - MathematicsGiven 7 flags of different colors, how many different signals can be generated if a signal requires the use of two flags, one below the other?

RD Sharma - Mathematics