Answer
Verified
425.1k+ views
Hint: A number to be divisible by 3, the sum of all the digits should be divisible by 3.
In this question, we are supposed to form a five digit number which will be divisible by 3, and the divisibility test of 3 is the sum of digits should be divisible by 3.
Therefore, we are only going to consider 5 digits whose sum will result in a number which will be divisible by 3.
Complete step-by-step answer:
Let us observe the digits given to us, we have 0,1,2,3,4 and 5, to make a five digit number we only need 5 digits out of the given 6 digits,
Case 1: Using digits 0,1,2,4 and 5.
The number of ways in which we can arrange these 5 digits are \[ \Rightarrow 4 \times 4 \times 3 \times 2 \times 1\]
\[ \Rightarrow 96\]
Case 2: Using the digits 1,2,3,4 and 5
The number of ways in which we can arrange these 5 digits are \[ \Rightarrow 5 \times 4 \times 3 \times 2 \times 1\]
\[ \Rightarrow 120\]
Therefore, the total number of cases $= 96+120 = 216$
Therefore, Option A is the correct answer.
Note: Make sure that you do not take 0 in the first place because that will make the number a 4-digit number which will be considered wrong as we are supposed to form a 5-digit number.
In this question, we are supposed to form a five digit number which will be divisible by 3, and the divisibility test of 3 is the sum of digits should be divisible by 3.
Therefore, we are only going to consider 5 digits whose sum will result in a number which will be divisible by 3.
Complete step-by-step answer:
Let us observe the digits given to us, we have 0,1,2,3,4 and 5, to make a five digit number we only need 5 digits out of the given 6 digits,
Case 1: Using digits 0,1,2,4 and 5.
The number of ways in which we can arrange these 5 digits are \[ \Rightarrow 4 \times 4 \times 3 \times 2 \times 1\]
\[ \Rightarrow 96\]
Case 2: Using the digits 1,2,3,4 and 5
The number of ways in which we can arrange these 5 digits are \[ \Rightarrow 5 \times 4 \times 3 \times 2 \times 1\]
\[ \Rightarrow 120\]
Therefore, the total number of cases $= 96+120 = 216$
Therefore, Option A is the correct answer.
Note: Make sure that you do not take 0 in the first place because that will make the number a 4-digit number which will be considered wrong as we are supposed to form a 5-digit number.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE