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

Redeem

In a certain mathematical activity, we start with seven cards, each with a different prime number written on it...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

In a certain mathematical activity, we start with seven cards, each with a different prime number written on it...

by BTGmoderatorLU » Thu Feb 13, 2020 3:24 am
Source: Magoosh

In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets can be created from this process?

A. 35
B. 105
C. 210
D. 420
E. 630

The OA is B
Top
Source: — Problem Solving |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: In a certain mathematical activity, we start with seven cards, each with a different prime number written on it...

by deloitte247 » Sun Feb 16, 2020 2:51 pm
Total no. of cards = 7
These 7 cards are randomly put into 3 different boxes.
Box 1 = gets 4 cards
The number of ways to choose 4 cards out of the 7 cards for box 1 = 7C4
Hence, box 1 gets 4 cards remaining card = 3
Box 2 = gets 2 cards
The number of ways to choose 2 cards from the remaining 3 cards = 3C2
Box 3 = gets the remaining 4
The number of ways to choose 1 card out of the remaining 1 = 1
Total no. of sets that can be created = (7C4) * (3C2) * 1
$$=\left[\frac{7!}{\left(7-4\right)!\cdot4!}\cdot\frac{3!}{\left(3-2\right)!\cdot2!}\right]\cdot1$$
$$=\left[\frac{7\cdot6\cdot5\cdot4!}{3\cdot2\cdot1\cdot4!}\right]\cdot\left[\frac{3\cdot2!}{1\cdot2!}\right]\cdot1$$
$$=\left[7\cdot5\right]\cdot\left[3\right]\cdot1=35\cdot3\cdot1=105$$
Answer = option B
Top
Post new topic Post Reply
• Page 1 of 1