The surface area (SA) of the triangular prism given above is the sum of its lateral area (LA) and the areas of its bases (BA).
SA = LA + 2 x BA
From the given above,
SA = 18 m² + 2 x 15 m² = 48 m²
Thus, the surface area of the solid is approximately 48 m².
Answer:
B
Step-by-step explanation:
When you have 3 choices for each of 6 spins, the number of possible "words" is
3^6 = 729
The number of permutations of 6 things that are 3 groups of 2 is
6!/(2!×2!×2!) = 720/8 = 90
A) The probability of a word containing two of each of the letters is 90/729 = 10/81
The number of permutations of 6 things from two groups of different sizes is
(2 and 4) : 6!/(2!×4!) = 15
(3 and 3) : 6!/(3!×3!) = 20
(4 and 2) : 15
(5 and 1) : 6
(6 and 0) : 1
B) The number of ways there can be at least 2 "a"s and no "b"s is
15 + 20 + 15 + 6 + 1 = 57
The probability of a word containing at least 2 "a"s and no "b"s is 57/729 = 19/243.
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These numbers were verified by listing all possibilities and actually counting the ones that met your requirements.
In this situation, the order matters, since being 1st pick is not the same as being 2nd or 3rd. Therefore, there are 14 choices for the first pick, 13 remaining for the second pick, and 12 for the third pick. This is equivalent to the permutation 12P3.
ways
(If order did not matter, this would use a combination.)