Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Among the 8! permutations of the digits 1,2, 3......... 8, con

Question

Among the $8!$ permutations of the digits $1, 2, 3.........8,$ consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by $5.$ The number of such arrangement is equal to

7!

2 (7!)

^{7} C_{4}

None of these

Views: 1,116 students

Found 4 tutors discussing this question

Mateo Discussed

Among the

8!

permutations of the digits

1, 2, 3.........8,

consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by

5.

The number of such arrangement is equal to

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

We have

8

positions the things is that the digit must be in first

5

position or last

5

position.

So,

5

must be fixed at either the

4 t h

place or

5 t h

place and after that

7!

combination of

7

digits are possible.

∴

No. of ways

= 2 \times 7!

Hence, the answer is

2 (7!) .

Was this solution helpful?

152

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Among the $8!$ permutations of the digits $1, 2, 3.........8,$ consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by $5.$ The number of such arrangement is equal to
Answer Type	Text solution:1
Upvotes	152

Among the 8! permutations of the digits 1,2,3.........8, consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by 5. The number of such arrangement is equal to

Text solutionVerified

Practice questions from similar books

Among the $8!$ permutations of the digits $1, 2, 3.........8,$ consider those arrangements which have the following property. If we take any five consecutive positions, the product of the digits in these positions is divisible by $5.$ The number of such arrangement is equal to