answer :

Formula:

nPr =n!  / (n1! n2! . . . nk!)

"PESAN" = 120 distinct ways to arrange different words.

• n = 5

• Subsets : P = 1; E = 1; S = 1; A = 1; N = 1;

• n1(P) = 1, n2(E) = 1, n3(S) = 1, n4(A) = 1, n5(N) = 1

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=5!  / (1! 1! 1! 1! 1! )

=1 x 2 x 3 x 4 x 5  / {(1) (1) (1) (1) (1)}

=120 / 1

= 120

In 120 distinct ways, the letters of word "PESAN" can be arranged.

"INI" = 3 distinct ways to arrange different words.

• n = 3

• Subsets : I = 2; N = 1;

• n1(I) = 2, n2(N) = 1

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nPr formula

=3!  / (2! 1! )

=1 x 2 x 3  / {(1 x 2) (1)}

=6  / 2

= 3

In 3 distinct ways, the letters of word "INI" can be arranged.

"MENGANDUNG" = 302400 distinct ways

• n = 10

• Subsets : M = 1; E = 1; N = 3; G = 2; A = 1; D = 1; U = 1;

• n1(M) = 1, n2(E) = 1, n3(N) = 3, n4(G) = 2, n5(A) = 1, n6(D) = 1, n7(U) = 1

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nPr formula

=10!  / (1! 1! 3! 2! 1! 1! 1! )

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10  / {(1) (1) (1 x 2 x 3) (1 x 2) (1) (1) (1)}

=3628800  / 12

= 302400

In 302400 distinct ways, the letters of word "MENGANDUNG" can be arranged.

"BAHASA" = 120 distinct ways

• n = 6

• Subsets : B = 1; A = 3; H = 1; S = 1;

• n1(B) = 1, n2(A) = 3, n3(H) = 1, n4(S) = 1

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nPr formula

=6!  / (1! 3! 1! 1! )

=1 x 2 x 3 x 4 x 5 x 6  / {(1) (1 x 2 x 3) (1) (1)}

=720  / 6

= 120

In 120 distinct ways, the letters of word "BAHASA" can be arranged.

"TERLARANG" = 90720 distinct ways

• n = 9

• Subsets : T = 1; E = 1; R = 2; L = 1; A = 2; N = 1; G = 1;

• n1(T) = 1, n2(E) = 1, n3(R) = 2, n4(L) = 1, n5(A) = 2, n6(N) = 1, n7(G) = 1

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nPr formula

=9!  / (1! 1! 2! 1! 2! 1! 1! )

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9  / {(1) (1) (1 x 2) (1) (1 x 2) (1) (1)}

=362880  / 4

= 90720

In 90720 distinct ways, the letters of word "TERLARANG" can be arranged.