How many strings of 6 letters can be made...

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Oct 27, 2017 6:33 am

How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?

A. 2Ã—3^6
B. 3Ã—2^6
C. 3Ã—3^6
D. 2Ã—2^6
E. 6^6

The OA is A.

Can any expert explain this PS question for me please? I don't understand it.

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Source: Beat The GMAT — Problem Solving | Fri Oct 27, 2017 6:33 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Fri Oct 27, 2017 8:13 am

LUANDATO wrote:How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?

A. 2 Ã— 3^6
B. 3 Ã— 2^6
C. 3 Ã— 3^6
D. 2 Ã— 2^6
E. 6^6

The OA is A.

Can any expert explain this PS question for me please? I don't understand it.

Number of ways we can make a 6-letter code using only A, B, and C: Well, we have 6 letters we need to select. For each selection, we'll have 3 options. So the number of codes we can make would be 3 * 3 * 3 * 3 * 3 * 3 = 3^6.

If we wish to make a 6-letter code using only D, E, and F, the math will be identical, and there will be another 3^6 options.

So now we have a total of 3^6 + 3^ 6, or 2 * (3^6) options. The answer is A

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