BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 bo

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Tue Jul 21, 2020 10:14 am

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 bo

by sambati » Tue Aug 04, 2020 1:53 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A 56
B 126
C 152
D 196
E 252
Top
Source: — Problem Solving |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select

by deloitte247 » Sat Aug 08, 2020 2:26 am
Total books = 10
Total small books = 8
Total large books = 2

In how many ways can Romi select 5 books to take with him on a trip if he can take at most 1 large book?

Since the maximum large book(s) he can take = 1
Therefore, he can select either - 5 small books or
- 4 small books and 1 large book

$$Selecting\ 5\ small\ book\ =\ 8C5$$
$$8C5\ =\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5\cdot4\cdot3\cdot2\cdot1\left(3\cdot2\cdot1\right)}$$
$$=\frac{8\cdot7\cdot6}{6}$$
$$=8\cdot7=56$$

$$Selecting\ 4\ small\ books\ and\ 1\ l\arg e\ book\ =\ 8C4\cdot2C1$$
$$8C4=\frac{8!}{4!\left(8-4\right)!}$$
$$\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{4\cdot3\cdot2\cdot1\left(4\cdot3\cdot2\cdot1\right)}$$
$$\frac{8\cdot7\cdot6\cdot5}{4\cdot3\cdot2\cdot1}=\frac{1680}{24}$$
$$=70$$
$$2C1=\frac{2!}{1!\left(2-1\right)!}=\frac{2\cdot1}{1\cdot1}=2$$
$$8C4\ \cdot\ 2C1\ =\ 70\cdot2=140$$


The total number of ways for Romi to select 5 books = 56 +140 = 196
Answer = D
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8085
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select

by Scott@TargetTestPrep » Tue Aug 18, 2020 10:27 am
sambati wrote: ↑
Tue Aug 04, 2020 1:53 pm
 Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A 56
B 126
C 152
D 196
E 252
Solution:

The number of ways he can take exactly 1 large book (along with 4 small books) is to choose 1 large book out of 2 available and 4 small books out of 8 available. Thus, we have: 2C1 x 8C4 = 2 x (8 x 7 x 6 x 5)/(4 x 3 x 2) = 2 x 7 x 2 x 5 = 140 ways.

The number of ways he can take no large book (and thus all 5 small books) is 2C0 x 8C5 = 1 x (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2) = 8 x 7 = 56.

Therefore, the total number of ways he can take at most 1 large book with him on the trip is 140 + 56 = 196.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1