How many different flags can be made from4 colors- Red, Blue

[BTGmoderatorDC]

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

OA E

Source: e-GMAT

[Jay@ManhattanReview]

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

OA E

Source: e-GMAT

"¢ No. of flags taking only one color at a time = 4;
"¢ No. of flags taking two colors at a time = 4P2 = 4*3 = 12;
"¢ No. of flags taking three colors at a time = 4P3 = 4*3*2 = 24;
"¢ No. of flags taking four colors at a time = 4P4 = 4*3*2*1 = 24

Total no. of flags = 4 + 12 + 24 + 24 = 64

The correct answer: E

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

OA E

Source: e-GMAT

The number of flags that can be made using 1 color only is 4P1 = 4.

The number of flags that can be made using exactly 2 colors is 4P2 = 4 x 3 = 12.

The number of flags that can be made using exactly 3 colors is 4P3 = 4 x 3 x 2 = 24.

The number of flags that can be made using all 4 colors is 4P4 = 4 x 3 x 2 x 1 = 24.

Therefore, the total number of flags that can be made is 4 + 12 + 24 + 24 = 64.

Answer: E