Question

Five friends a,b,c,d and e are sitting together.In how many ways can they sit so that b and c do not sit together?

Answer 1

Answer:

Five friends a,b,c,d and e are sitting together.

They can  sit in 72 ways so that b and c do not sit together?

Step-by-step explanation:

5 friends can sit together in

5 * 4 * 3 * 2 * 1 = 120 Ways

now let say b & c Sit together

(they can sit bc or cb) lets call it x

now we have a , d , e & x = 4

they can sit in

4 * 3 * 2 * 1 = 24 ways

but x can sit two ways bc or cb

24 * 2 = 48 ways  b&c will sit together

Number of ways so that b and c do not sit together = Total number of ways - number of ways  b&c will sit together

= 120 - 48

= 72 Ways

Answer 2

Answer :

They can  sit in 72 ways so that b and c do not sit together

Step-by-step explanation:

5 friends can sit together in 5! ways

⇒ Number of ways = 5 × 4 × 3 × 2 × 1

                                = 120 Ways

Now let say b & c sit together

So, They can sit together in two ways i.e. bc or cb

Now, we have 4 friends : a, d, e, and (bc or cb)

⇒ They can sit in 4! ways

⇒ Number of ways = 4 × 3 × 2 × 1

                                = 24 ways

Also, for two ways of bc or cb

⇒ Number of ways = 24 × 2

                                = 48 ways  b&c will sit together

Number of ways so that b and c do not sit together = Total number of ways - number of ways  b&c will sit together

= 120 - 48

= 72 Ways