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# There are a total of 10 sandwiches in a picnic hamper, 5 of which are

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4106
GPA: 3.39
There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink]

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04 Mar 2019, 14:42
1
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:24) correct 17% (01:40) wrong based on 35 sessions

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There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed?

A. $$\frac{3}{10}$$

B. $$\frac{2}{45}$$

C. $$\frac{3}{80}$$

D. $$\frac{1}{27}$$

E. $$\frac{1}{120}$$

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Joined: 04 Jan 2015
Posts: 3074
Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink]

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04 Mar 2019, 23:03
1

Solution

Given:
• There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey.
• 3 sandwiches are removed at random.

To find:
• The probability that all 3 roast beef sandwiches are removed.

Approach and Working:
• The number of ways we can remove 3 sandwiches from a total of 10 sandwiches = $$^{10}C_3$$ = 120
• The number of ways we can remove 3 roast beef sandwiches from a total of 3 roast beef sandwiches = $$^3C_3$$ = 1
• Therefore, the required probability = $$\frac{1}{120}$$

Hence, the correct answer is option E.

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Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink]

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06 Mar 2019, 02:17
total sandwiches = 10
so beef being removed = 3/10 * 2/9 * 1/8
1/120
IMO E

There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed?

A. $$\frac{3}{10}$$

B. $$\frac{2}{45}$$

C. $$\frac{3}{80}$$

D. $$\frac{1}{27}$$

E. $$\frac{1}{120}$$
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Joined: 14 Oct 2015
Posts: 8086
Location: United States (CA)
Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are  [#permalink]

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08 Mar 2019, 08:02
There are a total of 10 sandwiches in a picnic hamper, 5 of which are ham, 3 of which are roast beef, and 2 of which are turkey. If 3 of the sandwiches are removed at random, what is the probability that all 3 roast beef sandwiches are removed?

A. $$\frac{3}{10}$$

B. $$\frac{2}{45}$$

C. $$\frac{3}{80}$$

D. $$\frac{1}{27}$$

E. $$\frac{1}{120}$$

The probability that 3 beef sandwiches are removed is (3C3)/(10C3) = 1/[(10 x 9 x 8)/3!] = 1/120.

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Re: There are a total of 10 sandwiches in a picnic hamper, 5 of which are   [#permalink] 08 Mar 2019, 08:02
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