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A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of 8 flags that can be made using 4 white flags, 2 red flags, and 2 blue flags

Respuesta :

Stephaniereplogle

Answer:

420

Step-by-step explanation:

(8*7*6*5)/(2*2)

fichoh

Using the principle of permutation, the number of distinguishable arrangement of flags which can be made is 420.

The number of ways of arranging 8 flags is given thus :

  • 8! = 8×7×6×5×4×3×2×1 = 40320

The number of arrangement of each colored flag :

  • White flag = 4! = 4×3×2×1 = 24
  • Red flag = 2! = 2×1 = 2
  • Blue flag = 2! = 2×1 = 2

The number of distinguishable permutations :

40320 ÷ (24 × 2 × 2)

40320 ÷ (96)

= 420

Therefore, there are 420 different signals which can be made.

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