Problem Solving (PS) | Re: How many 3-letter codes can be formed by choosing, without replacement

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A 3 letter code out of PEPPER can be made in 3 differentways.

All 3 letters the same.
The code is PPP. Nothing else is possible. So 1code.

2 letterssame.
Select the  letter to be repeated in 2 ways (either P or E). Select the third letter in 2 ways (R or leftover letter).
Arrange all letters in 3 different ways (e.g. PPR, PRP, RPP)
Total codes = 2 * 2 * 3 =12

No lettersame.
We have only 3 distinct letters (P, E, R) so all 3 must be taken. 
We can arrange them in 3! ways = 6 codes

Total number of codes = 1 + 12 + 6 =19

Answer(C) 

Video on Permutations:
https://youtu.be/LFnLKx06EMU

Video on Combinations:
https://youtu.be/tUPJhcUxllQ
 
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Statistics : Posted by KarishmaB • on 19 Nov 2023, 17:24 • Replies 7 • Views 6659

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