A Group Of 4 Soldiers,6 Policeman, And 5 Generals Are To Be Seated In A Row Of 15 Seats.In How Many Mays Can They Be Seated Given The Following Condit

A group of 4 soldiers,6 policeman, and 5 generals are to be seated in a row of 15 seats.In how many mays can they be seated given the following conditions: 1. The generals are to be seated next to each other. #2. Two of soldiers are on one end and the other two on the other end of the row. #3. The policeman are seated in a consicutive seats.

 

Answer:

Step-by-step explanation:

Condition #1: Generals are to be seated next to each other.

Take the 5 generals as a single unit and there will 11 factorial arrangements which will be multiplied to 5 factorial ways between the generals.

11! × 5! = (11×10×9×8×7×6×5×4×3×2×1)(5×4×3×2×1) = (39,916,800)(120) = 4,790,016,000

Condition #2: Two of soldiers are on one end and the other two on the other end of the row.

Consider the 2 soldiers on one end and the 2 on the other end as a single row of 4 seats. Let 4 factorial stand for their arrangements to be multiplied by 11 factorial ways of 6 policemen and 5 generals in the remaining 11 seats.

4! × 11! = (4×3×2×1)(11×10×9×8×7×6×5×4×3×2×1) = (24)(39,916,800) = 958,003,200

Condition #3: The policemen are seated in consecutive seats.

Take the 6 policemen as a single unit with 6 factorial as their arrangements to be multiplied by 10 factorial ways.

6! × 10! = (6×5×4×3×2×1)(10×9×8×7×6×5×4×3×2×1) = (720)(3,628,800) = 2,612,736,000