gmatbeater1989 wrote:I tried using the slot method here but didn't get very far. Can you use it with this question?
Let the six positions be as follows:
BACK _ _ _ _ _ _ FRONT
Since F must stand behind J, J must be positioned to the right of F.
Case 1: F _ _ _ _ _
Since the 5 remaining slots may be occupied by any arrangement of the 5 remaining mobsters, the slots look as follows:
F *
5 * 4 * 3 * 2 * 1.
Multiplying the values in red, we get;
5*4*3*2*1 = 120.
Case 2: _ F _ _ _ _
Number of options for the first slot = 4. (Of the 5 remaining mobsters, anyone but J.)
Since the 4 remaining slots may be occupied by any arrangement of the 4 remaining mobsters, the slots look as follows:
4 * F *
4 * 3 * 2 * 1.
Multiplying the values in red, we get;
4*4*3*2*1 = 96.
Case 3: _ _ F _ _ _
Number of options for the first slot = 4. (Of the 5 remaining mobsters, anyone but J.)
Number of options for the second slot = 3. (Of the 4 remaining mobsters, anyone but J.)
Since the 3 remaining slots may be occupied by any arrangement of the 3 remaining mobsters, the slots look as follows:
4 * 3 * F *
3 * 2 * 1.
Multiplying the values in red, we get;
4*3*3*2*1 = 72.
Case 4: _ _ _ F _ _
Number of options for the first slot = 4. (Of the 5 remaining mobsters, anyone but J.)
Number of options for the second slot = 3. (Of the 4 remaining mobsters, anyone but J.)
Number of options for the third slot = 2. (Of the 3 remaining mobsters, anyone but J.)
Since the 2 remaining slots may be occupied by any arrangement of the 2 remaining mobsters, the slots look as follows:
4 * 3 * 2 * F *
2 * 1.
Multiplying the values in red, we get;
4*3*2*2*1 = 48.
Case 5: _ _ _ _ F J
Since the 4 remaining slots may be occupied by any arrangement of the 4 remaining mobsters, the slots look as follows:
4 * 3 * 2 * 1 * F * J.
Multiplying the values in red, we get;
4*3*2*1 = 24.
Total ways = 120 + 96 + 72 + 48 + 24 = 360.
The methods offered in the posts above seem faster.
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