The organizers of a week-long fair have hired exactly five security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
A) 9
B) 7
C) 5
D) 3
E) 2
Don't know the OA. This is how I did it and got D as the answer. It'd be great if someone can confirm if I'm right.
Monday to Saturday comprises of 6 nights.
Monday - we have 5 guards and 2 to be selected. So, 5C2 = 10 ways
Tueday - 2 guards from Monday cannot be selected. So, 3C2 = 3 ways
Wednesday - Again, 2 guards from Tue cant be chosen but the 2 from Monday are now available.
So, 3C2 = 3 ways
The same process repeats till Saturday. So on Saturday night as well, we'll have 3 pairs to select.
A) 9
B) 7
C) 5
D) 3
E) 2
Don't know the OA. This is how I did it and got D as the answer. It'd be great if someone can confirm if I'm right.
Monday to Saturday comprises of 6 nights.
Monday - we have 5 guards and 2 to be selected. So, 5C2 = 10 ways
Tueday - 2 guards from Monday cannot be selected. So, 3C2 = 3 ways
Wednesday - Again, 2 guards from Tue cant be chosen but the 2 from Monday are now available.
So, 3C2 = 3 ways
The same process repeats till Saturday. So on Saturday night as well, we'll have 3 pairs to select.
Regards,
Sunit
________________________________
Kill all my demons..And my angels might die too!
Sunit
________________________________
Kill all my demons..And my angels might die too!
