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Combinatorics: 9. Three young brother-sister pairs from different families need to take a trip in a van. These six children will occupy the second and third rows in the van, each of which has three seats. To avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit directly in front of his or her sibling. How many seating arrangements are possible for this trip?

Combinatorics: 9. Three young brother-sister pairs from different families need to take a trip in a van. These six children will occupy the second and third rows in the van, each of which has three seats. To avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit directly in front of his or her sibling. How many seating arrangements are possible for this trip?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Combinatorics: 9. Three young brother-sister pairs from different families need to take a trip in a van. These six children will occupy the second and third rows in the van, each of which has three seats. To avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit directly in front of his or her sibling. How many seating arrangements are possible for this trip? 10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 = 5 has two divisors (1 and 5 itself) 6 = 2* x 3 has four divisors (1, 2, 3 and 6) 16 = 2 has five divisors (1, 2, 4, 8 and 16). a d-1 If a number n = p, X .. X Px p, where p, P, P3 P Pare prime numbers and a, a,, a. a,, a are the corresponding exponents of the prime numbers, how p. 2 3 k-1 k α. many divisors does n have ? 11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
Transcribed Image Text:Combinatorics: 9. Three young brother-sister pairs from different families need to take a trip in a van. These six children will occupy the second and third rows in the van, each of which has three seats. To avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit directly in front of his or her sibling. How many seating arrangements are possible for this trip? 10. Every positive integer greater than 1 has at least two divisors and can be written as a unique product of some prime number/s with exponents. For example, 5 = 5 has two divisors (1 and 5 itself) 6 = 2* x 3 has four divisors (1, 2, 3 and 6) 16 = 2 has five divisors (1, 2, 4, 8 and 16). a d-1 If a number n = p, X .. X Px p, where p, P, P3 P Pare prime numbers and a, a,, a. a,, a are the corresponding exponents of the prime numbers, how p. 2 3 k-1 k α. many divisors does n have ? 11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
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