Example 1.2-12 A coin is flipped 10 times and the sequence of heads and tails is

Question

Example 1.2-12 A coin is flipped 10 times and the sequence of heads and tails is observed. The num- ber of possible 10-tuplet that result in four hands and six tails is Example 1.2-13 In an orchid show, seven orchids are to be placed along one side of the greenhouse. There are four lavender orchids and three white orchids. Considering only the color of the orchids, we see that the number of lineups of the orchids is If the colors of the seven orchids are while, lavender, yellow, mauve, crimson, orange, and pink, the number of different displays is Example 1.2-14 Among nine orchids of a line of orchids along one wall, three are white, four lavender, and two yellow. The number of different color displays is then_ Select 4 positions from the remaining positions in_ways Select 2 positions from the remaining positions in ways. Finally, use the multiplication rule. Summary: Suppose that a set contains n objects of two types: r of one type and n-r of the other type.

Explanation / Answer

1.2-12 A Number of ways to get four heads and six tails = 10! / (4! * 6!) = 210

1.2-13 Number of lineup of 4 lavender & 3 white orchids = 7! /(4! * 3!) = 35

Number of different display of seven colors of orchids = 7! = 5040

1.2-14 The number of different color display of 3 white, 4 lavender and 2 yellow orchids = 9!/ (3! * 4! * 2!) = 1260

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