Q. 114.0( 1 Vote )

# Mark the correct alternative in the following:

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

A. 24

B. 30

C. 125

D. 100

Answer :

We know, any number to be divisible by 4, we must have the last 2 digits of the number divisible by 4.

So, the whole four-digit number will be divisible by 4 if the last 2 digits are: 12, 32, 52, 24.

__Case-1:__ When, we have 2 in ones’ place:

In this case, we can fill tens’ place with 1 ,3 or 5 i.e. we have 3 ways to fill the tens’ place.

Hundreds’ place can be filled with any 2 of the remaining 3 digits [2 digits are used to fill the ones’ and tens’ place among the given 5 digits], in ^{3}P_{2} = 6 ways.

So, number of four-digit numbers that can be formed in this case

= 18.

__Case-2:__ When, we have 4 in ones’ place:

In this case, we can fill tens’ place with 2 i.e. tens’ place can be filled only in 1 way.

Hundreds’ place can be filled with any 2 of the remaining 3 digits [2 digits are used to fill the ones’ and tens’ place among the given 5 digits], in ^{3}P_{2} = 6 ways.

So, number of four-digit numbers that can be formed in this case = 6.

As, the two cases are independent so, the total number of four-digit numbers that can be formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is = 18 + 6

= __24__.

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