Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
How many ways are there in putting 5 different books into 2 different bags so that each bag contains at least 1 book?
 one year ago
 one year ago
How many ways are there in putting 5 different books into 2 different bags so that each bag contains at least 1 book?
 one year ago
 one year ago

This Question is Closed

estudierBest ResponseYou've already chosen the best response.0
First put 1 book in each bag.
 one year ago

orderBest ResponseYou've already chosen the best response.1
This is a long process without formula... however, if you want to be certain, try formulas with Combinations and Permutations, and list out all the ways if you have time.. Head start on the listing: 5 different books = a,b,c,d,e Bags= B1, B2 B1~~B2 a ~~ b a ~~ c a ~~ d a ~~ e ab~~c ab~~d ab~~e and so forth.. Not sure with the formulas, but you could try something like \[^5P_2\]
 one year ago

orderBest ResponseYou've already chosen the best response.1
But am sure just plugging those in won't give the correct answer... See what you can do..
 one year ago

kropot72Best ResponseYou've already chosen the best response.0
Consider bag A. The number of combinations of books taken one at a time = 5!/4! =5 The number of combinations of books taken two at a time = 5!/(2*3!) = 10 The number of combinations of books taken three at a time = 5!/(3!*2!) = 10 The number of combinations of books taken four at a time = 5!/4! = 5 The total number of allowed combinations of books in bag A = 5 + 10 + 10 + 5 = 30 The total number of allowed combinations of books in bag B will also equal 30. Therefore the total number of ways of putting the five different books into two different bags so that each bag contains at least one book = 30 + 30 = 60 ways
 one year ago

KaederfdsBest ResponseYou've already chosen the best response.2
dw:1336274424353:dw I think
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
1 4; 5ways 2 3 =*(1, 3) 4 ways 5 times 3 2 ; same as above 4 1; same as above 2*5 + 2*(4*5) = 10 + 40 = 50 maybe :)
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
but that middle has a few duplicates that would need to be weeded out
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
ab cde ac bde ad cbe ae dcb bc dea bd cea be dca ba cde ** duplicate cd eab ce dab ca edb ** duplicate cb dea ** duplicate de abc da ** db ** dc ** ea ** eb ** ec ** ed ** 10 ways ... to stack 2,3
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
10+10+5+5 = 30 different ways ... maybe ;)
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
5c1 + 5c2 + 5c2 + 5c1 = 30
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
5c1 + 5c2 + 5c3 + 5c4 = 30 might conform to the structure better tho
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.