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# How many three-digit numerals begin With a digit that represents a pri

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How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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12 Nov 2018, 10:26
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25% (medium)

Question Stats:

73% (01:17) correct 27% (01:38) wrong based on 240 sessions

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How many three-digit numerals begin With a digit that represents a prime number and end with a digit that represents a prime number?

(A) 16
(B) 80
(C) 160
(D) 180
(E) 240

Project PS Butler : Question #14

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Re: How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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12 Nov 2018, 10:41
4
Let number be X X X. First and last spots can be taken by 2, 3, 5, 7, so 4 numbers for each spot. Middle spot can be taken by any of the 10 digits.

So, my guess is 4*10*4 = 160 is the answer.

Option C
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Re: How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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13 Nov 2018, 02:22
1
1
HKD1710 wrote:
How many three-digit numerals begin With a digit that represents a prime number and end with a digit that represents a prime number?

(A) 16
(B) 80
(C) 160
(D) 180
(E) 240

Project PS Butler : Question #14

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The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem. Basically, you multiply the events together to get the total number of outcomes. The formula is:
If you have an event “a” and another event “b” then all the different outcomes for the events is a * b. "AND" means multiplication

Source: https://www.statisticshowto.datascience ... principle/

So,
Stage 1. 4 numbers ( 2, 3, 5, 7)
Stage 2. 10 numbers ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Stage 3. 4 numbers (2, 3, 5, 7)
Stage 4. Kill that annoying fly that is buzzing around your office

$$4*10*4 = 160$$

pushpitkc, how are you there ? i have one question to clear my confusions when do i need to use slot method ? i also was thinking like this:

4 numbers in 4! ways
10 numbers in 10! ways
4 numbers in 4! ways!

4!*10!*4!
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Re: How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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13 Nov 2018, 05:09
1
dave13 if I may chip in my two cents,

You have to use factorial to list out the possibke permutations in an order.

Here you are just selecting numbers ( digits of a three digit number with constraints)

So your answer is almost correct albeit the factorial sign.

4 ways to choose a prime.

The three digit number will begin and end with a prime and the middle digit will have 10 options.

Hence, 4*10*4 = 160

Does this make sense?

Best,
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Re: How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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24 Nov 2018, 03:57
dave13 if I may chip in my two cents,

You have to use factorial to list out the possibke permutations in an order.

Here you are just selecting numbers ( digits of a three digit number with constraints)

So your answer is almost correct albeit the factorial sign.

4 ways to choose a prime.

The three digit number will begin and end with a prime and the middle digit will have 10 options.

Hence, 4*10*4 = 160

Does this make sense?

Best,

No ways to select the first no is 4
no of ways to select middle no is 10
Why is the no ways to select the third no is 4 and not 3? If we select 4, are not we repeating same combination?
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Re: How many three-digit numerals begin With a digit that represents a pri  [#permalink]

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08 Jun 2019, 03:50
aghosh54 wrote:
dave13 if I may chip in my two cents,

You have to use factorial to list out the possibke permutations in an order.

Here you are just selecting numbers ( digits of a three digit number with constraints)

So your answer is almost correct albeit the factorial sign.

4 ways to choose a prime.

The three digit number will begin and end with a prime and the middle digit will have 10 options.

Hence, 4*10*4 = 160

Does this make sense?

Best,

No ways to select the first no is 4
no of ways to select middle no is 10
Why is the no ways to select the third no is 4 and not 3? If we select 4, are not we repeating same combination?

yes we are repeating it,
but thats okay, according to the condition...
Start with a prime digit, and end with a prime digit, doesn't say, "it can't have repeating prime digits"
then, the answer will be 4*10*3 = 120
I guess so

here the answer is fine, 4*10*4 = 160.
Re: How many three-digit numerals begin With a digit that represents a pri   [#permalink] 08 Jun 2019, 03:50
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# How many three-digit numerals begin With a digit that represents a pri

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