The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges is

Intern

Joined: 18 Aug 2005

Posts: 15

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 piece [#permalink]

26 Nov 2005, 12:27

00:00

Question Stats:

0% (00:00) correct

100% (00:40) wrong

based on 23 sessions

Hide Show timer Statistics

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, talking at least one of each kind.

GMAT Expert

Joined: 16 Oct 2010

Posts: 13138

Location: Pune, India

Re: From 4 oranges, 3 bananas and 2 apples, how many selections of 5 piece [#permalink]

31 Aug 2019, 01:13

sandman wrote:

From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, talking at least one of each kind.

Please post a screenshot of the exact question. I am not sure whether the fruits are to be taken as identical or distinct e.g. whether the 4 oranges are identical or distinct. If nothing is given, I would be tempted to take them as identical. In that case, I would split 5 into 3 groups with at least one each in the following ways:{3, 1, 1} - 2 ways (3 oranges or 3 bananas){2, 2, 1} - 3 ways (1 orange or 1 banana or 1 apple)So 5 ways. But if the fruit pieces are distinct, then we have 9 distinct pieces of which we have to select 5 in 9C5 ways.Out of these 9C5 ways, you are not allowed those in which one type of fruit is not taken. No of ways in which oranges are not taken = 5C5No of ways in which bananas are not taken = 6C5No of ways in which apples are not taken = 7C5So total acceptable ways = 9C5 - 5C5 - 6C5 - 7C5 = 126 - 1 - 6 - 21 = 98 _________________

KarishmaOwner of Angles and Arguments at https://anglesandarguments.com/

NOW PUBLISHED - DATA SUFFICIENCY MODULE

For Individual GMAT Study Modules, check Study Modules >

For Private Tutoring, check Private Tutoring >

Director

Joined: 05 Apr 2005

Posts: 928

Re: From 4 oranges, 3 bananas and 2 apples, how many selections of 5 piece [#permalink]

26 Nov 2005, 22:03

total combinations = (a + b + 3o), (a + 2b + 2o), (a + 3b + o), (2a + b + 2o), (2a + 2b + 1o) possible numbers of combinations = (2c1 x 3c1 x 4c3) + (2c1 x 3c2 x 4c2) + (2c1 x 3c3 x 4c1) + (2c2 x 3c1 x 4c2) + (2c2 x 3c2 x 4c1) = (2x3x4) + (2x3x6) + (2x1x4) + (1x3x6) + (1x3x4) =24 + 36 + 8 + 18 + 12

= 98

Director

Joined: 14 Sep 2005

Posts: 650

Location: South Korea

Re: From 4 oranges, 3 bananas and 2 apples, how many selections of 5 piece [#permalink]

27 Nov 2005, 07:24

You buy at least one of each kind. Number of oranges you can choose from = 4 -1 = 3 Number of bananas you can choose from = 3 - 1 = 2 Number of apples you can choose from = 2 - 1 = 1 ------------------------------------------------------------ Total number of fruits you can choose from = 6 As you already have 3 fruits (one orange, one banana, and one apple), you need to pick 2 more fruits.

6C2 = 15

GMAT Club Legend

Joined: 18 Aug 2017

Status:You learn more from failure than from success.

Posts: 7163

Location: India

Concentration: Sustainability, Marketing

GPA: 4

WE:Marketing (Energy and Utilities)

Re: From 4 oranges, 3 bananas and 2 apples, how many selections of 5 piece [#permalink]

29 Aug 2019, 06:27

sandman wrote: