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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, 09:26
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00:00

Difficulty:

35% (medium)

Question Stats:

78% (01:08) correct 22% (01:17) wrong based on 81 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, 09:41
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, 01:22
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

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, 04:09
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)

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, 02:57
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)

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 &nbs [#permalink] 24 Nov 2018, 02:57
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