## dydlf 2 years ago heeelp! in how many ways can 2 elephants, 1 monkey and 3 ants sit in a row if no 2 animals of the same kind are together? assume 2 animals of the same kind are distinguishable. answer is said to be 120. O:

1. cammyabbo

this is a permutations questions

2. cammyabbo

you have 6 animals, 2 are the same and 3 are the same

3. dydlf

they're considered distinguishableO: so not really the "same"

4. cammyabbo

the answer would be 720 if that was the case

5. cammyabbo

6. dydlf

the book says 120 :(

7. cammyabbo

is it DISTINGUISHABLE, or INdistinguishable

8. dydlf

distinguishiable O:

9. shubhamsrg

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10. yrelhan4

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11. matricked

first arrange the elephants and the ants in the way such that the elephants are in betweeb the ants as such A1 E1 A2 E2 A3 which can be done in 3!*2! ways now the monkey can be paired with any of the five animals in 5*2! ways =10 e.g A1 E1M1 A2 E2 A3 & A1 M1E1 A2 E2 A3 (here paired with E1) another one paired with A3 A1 E1 A2 E2 A3 M1 & A1 E1 A2 E2 M1A3 in this way the number of ways is 3!*2!*(10)=120 (as no two animals of same kind are together)

12. matricked

@dydlf is it wrong ...

13. shubhamsrg

possible no. of arrangements of 3 ants is : 1) a_a_a_ -> 3! * 3! 2) a__a_a ->(3! * 3!) - ( 3! * 2!) 3) a_a__a -> (3! * 3!) - (31 * 2!) 4) _a_a_a -> 3! *3! so final answer= 36 +24 +36+ 24 = 120