wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The number of seven-digit integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is?


A

55

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

66

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

77

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

88

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

77


Explanation for correct option:

Finding the number of ways formed by the seven-digit number by using the digits 1,2 and 3 that sum is equal to 10 .

Let us consider,

We can divide the number 10 in two ways by using the digits 1,2 and 3 there are,

Case I: 1,1,1,1,1,2,3

Case II: 2,2,2,1,1,1,1

Thus,

Case I: The number of ways a seven-digit number can be formed:

The number of places to be filled is equal to 7and the number of repetitions is equal to 5, this can be expressed as

7!5!7×6×5!5!42

Case II: The number of ways a seven-digit number can be formed:

The number of places to be filled is equal to 7and the number of repetitions is equal to 3 and 4, for the numbers 2and1, respectively, this can be expressed as

7!3!×4!7×6×5×4!3×2×1×4!35

The total number of ways is,

42+35=77

Therefore, the correct answer is Option C.


flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basics of Division
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon