(a) In a dog show it is claimed that a dog could read the words Zero', One', "Two', 'Three', 'Four', 'Five', 'Six', 'Seven', 'Eight', 'Nine' written on 10 different cards. The dog is supposed to pick 10 bones numbered 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in the same order as the words on the cards are arranged. A member of the audience has arranged 3 cards in the order 'Nine', 'Zero' and "Two'. In how many ways can the dog fail to pick the numbered bones correctly? [The dog is considered to have failed even if only one error occurs]. (b) In the table below, the number of black and white buttons in three boxes A, B and C are all distinct. Воx Colour A B Black 3 6 4.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 54SE: How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and...
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In a dog show it is claimed that a dog could read the words 'Zero', "One',
"Two', "Three', 'Four', 'Five', 'Six', Seven', 'Eight', 'Nine' written on 10
different cards. The dog is supposed to pick 10 bones numbered 0, 1, 2, 3, 4, 5,
6, 7, 8 and 9 in the same order as the words on the cards are arranged. A
member of the audience has arranged 3 cards in the order 'Nine', 'Zero' and
Two'. In how many ways can the dog fail to pick the numbered bones
correctly? [The dog is considered to have failed even if only one error occurs].
(a)
(b)
In the table below, the number of black and white buttons in three boxes A, B
and C are all distinct.
Воx
Colour
A
B
Black
3
6.
5
White
7
4
(i)
All the buttons in box A are arranged in a row such that the 3 black
buttons are together. In how many different arrangements can this be
done?
A button is drawn from each of the boxes. If all the buttons drawn are
of the same colour, in how many ways can this be done?
(ii)
4.
Transcribed Image Text:In a dog show it is claimed that a dog could read the words 'Zero', "One', "Two', "Three', 'Four', 'Five', 'Six', Seven', 'Eight', 'Nine' written on 10 different cards. The dog is supposed to pick 10 bones numbered 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in the same order as the words on the cards are arranged. A member of the audience has arranged 3 cards in the order 'Nine', 'Zero' and Two'. In how many ways can the dog fail to pick the numbered bones correctly? [The dog is considered to have failed even if only one error occurs]. (a) (b) In the table below, the number of black and white buttons in three boxes A, B and C are all distinct. Воx Colour A B Black 3 6. 5 White 7 4 (i) All the buttons in box A are arranged in a row such that the 3 black buttons are together. In how many different arrangements can this be done? A button is drawn from each of the boxes. If all the buttons drawn are of the same colour, in how many ways can this be done? (ii) 4.
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