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# "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products

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"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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26 Sep 2015, 10:00
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

57% (02:08) correct 43% (02:15) wrong based on 108 sessions

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"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20

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Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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26 Sep 2015, 15:00
2
IMO: D - 19

There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.

The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).

#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1

9 + 9 + 1 = 19
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Joined: 29 Jul 2015
Posts: 158
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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26 Sep 2015, 17:09
1
reto wrote:
"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20

Number of combinations with pink color:-
Colours available after choosing pink are purple,orange,silver,blue and red. 2 colors are to be chosen.
Number of ways of choosing 2 colours out of 5 is 5C2 = 10

Number of combinations with purple colour:-
Colours available after choosing purple are orange,silver,blue and red.
Number of ways of selecting 2 colours out of 4 is 4C2= 6

Number of combinations with orange colour:-
Colours available after choosing orange are silver,blue and red.
Number of ways of selecting 2 colours out of 3 is 3C2= 3

Total number of combinations are 10+6+3 = 19

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Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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26 Sep 2015, 20:46
There are three cases possible.

Case 1: Only one of the three strip is Orange, pink or purple. Selection of one of these would be 3C1 = 3
The other two empty slots would mean selecting two from the remaining three i.e 3C2=3

Now, we need one of the desired three AND one of two of the other three. That means m ways of doing something and n ways of soing something else together would give me m*n ways. SO ( ways for case 1

Case 2: Reverse of the case above i.e 2 from the desired lot and 1 from the other lot. This gives 3C2 * 3C1 = 9

Case 3: All three are from the desired lot. As, the order is not important, hence only one way of doing so =1

Therefore, total 19 ways of doing so. D.
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Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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03 Oct 2015, 19:58
Total Choices are 6C3 = 20
Forbidden Choices aka (no options include pink, purple or orange) = 3C3 = 1

TC-FC = 20-1 = 19

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Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

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14 Feb 2018, 09:53
reto wrote:
"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20

We can use the formula:

Total number of ways to select 3 stripes - number of ways to select stripes without pink, purple or orange = number of ways with at least one of pink, purple or orange

Total number of ways to select 3 stripes:

6C3 = 6!/[3!(6-3)!] = 6!/(3!3!) = (6 x 5 x 4)/(3 x 2 x 1) = 20

The only way to choose 3 stripes, none of which is pink, purple, or orange, is if the 3 stripes are red, blue, and silver. Thus, the total number of ways to select stripes without pink, purple or orange:

3C3 = 1

So the number of ways with at least one of pink, purple or orange is 20 - 1 = 19.

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Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products &nbs [#permalink] 14 Feb 2018, 09:53
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