determine the number of permutations of {a, b, c, d, e} that satisfy the following conditions: (a) a occupies the first position. (b) a occupies the first position, and b the second. (c) a appears before b.

Respuesta :

The total number of ways/ permutation that A occupies first position is 24 ,  A occupies the first position, and B the second is 6 and a appears before b is 10 ways.

What is permutation ?

Permutation is a meeting of objects in an exceedingly definite order. The members or components of sets square measure organized here in an exceedingly sequence or linear order.

Main body:

A) a occupies the first position-

As A is first, and arrange the remaining letters.  letters (B,C,D,E,F) can be arranged as-

4*3*2*1 = 24 ways

B) a occupies the first position, and b the second

As A is first and b is just after it , there are 5 position out of which 2 are taken by A, B in order , so number of ways they can be arranged is

3*2*1 = 6 ways

C) a appears before b

in this part there is no  condition that a appears just before b , so b can be places anywhere after A.

after fixing A at first place , B can be placed at 4 places.

after fixing A at 2nd place , B can be placed at 3 places.

after fixing A at 3rd place , B can be placed at 2 places.

after fixing A at 4th  place , B can be placed at 1 places.

total ways = 4+3+2+1 = 10

Hence the answer to these parts are 24, 6,10

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