Hello!
.
The answer to your question is 495 ways.
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n = 12
r = 4
.
nCr = n1 / (n-r)! r1
12C4 = 12! / (12-4)! 4!
12C4 = 12x11x10x9x8! / 8! 4!
12C4 = 11880 / 24
12C4 = 495
:)
X is multiple of 9 as well as 12.
Thus, smallest value will be 36 ( 9 *4 = 36, 12 * 3 = 36)
3 and 12 are not the multiples of 9.
72 is a larger multiple than 36; thus, the correct answer is 36.
see the attached figure to better understand the problem
we have that

Step 1
<u>Find the value of AC</u>
we know that
in the right triangle ABC

substitute the values in the formula

Step 2
<u>Find the value of BC</u>
we know that
in the right triangle ABC
Applying the Pythagorean Theorem

substitute the values

Step 3
<u>Find the value of BD</u>
we know that
in the right triangle BCD
Applying the Pythagorean Theorem

substitute the values


therefore
<u>the answer is</u>
the length of BD is 11.93 units
Total: $125


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