Five boys and five girls form a line with the boys and girlsalternating. Find the number of ways of making the line.A. `(5!)^(2)`B. `10!`C. `5!+5!`D. `2(5!)^(2)`

Five boys and five girls form a line with the boys and girlsalternatin

1.	Five boys and five girls form a line with the boys and girlsalternating. Find the number of ways of making the line.A. `(5!)^(2)`B. `10!`C. `5!+5!`D. `2(5!)^(2)`
Answer» 5 boys can be arranged in a linen in 5! Ways. Since the boys and girls are alternating. So, corresponding each of the 5! Ways of arrangements of 5 boys we obtain 5 places marked by cross as shown below: (i) `B_(1)xxB_(2)xxB_(3)xxB_(4)xxB_(5)` (ii) `xxB_(1)xxB_(2)xxB_(3)xxB_(4)xxB_(5)` Clearly, 5 girls can be arranged in 5 places marked by cross in `(5!+5!)` ways. Hence, the total number of ways of making the line `=5!xx(5!+5!)=2(5!)^(2)`

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Five boys and five girls form a line with the boys and girlsalternating. Find the number of ways of making the line.A. `(5!)^(2)`B. `10!`C. `5!+5!`D. `2(5!)^(2)`

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