Specialist Mathematics · Unit 1 · Combinatorics · Introduction to counting techniques
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A security system requires a four-digit access code where the first digit must be odd, the second digit must be even, the third digit can be any digit, and the fourth digit must be different from the third digit. Use the multiplication principle to determine how many distinct access codes are possible.
How many distinct three-digit codes can be formed using the diagram shown, where the first digit must be selected from Set A, the second digit from Set B, and the third digit from Set C?
A restaurant offers a three-course set menu where diners must select one item from each course. The menu options are displayed in the table below. a) Use the multiplication principle to determine the total number of different three-course meal combinations available. (1 mark) b) If the restaurant adds two additional dessert options to the menu, determine how many more meal combinations become available. (1 mark) c) The restaurant decides to remove the Pâté and Salad from the entrée menu. Determine the number of different three-course meal combinations available with the reduced entrée selection. (1 mark)
How many distinct three-digit codes can be formed using the diagram shown, where the first digit is selected from Set A, the second digit from Set B, and the third digit from Set C?
A security system requires a code consisting of three components in sequence: a letter from the set {A, B, C, D, E, F}, a two-digit number from 10 to 99 inclusive, and a symbol from the set {#, @, *, &}. The system has the following restrictions: if the letter is a vowel (A or E), the two-digit number must be even; if the letter is a consonant, there are no restrictions on the number. Use the multiplication principle to determine the total number of distinct codes that can be formed under these restrictions.
Calculate the number of distinct three-digit codes that can be formed using the diagram shown.
A restaurant offers a three-course set menu where diners must select one item from each course. The menu options are displayed in the table below. a) Use the multiplication principle to determine the total number of different three-course meal combinations available. (1 mark) b) If the restaurant adds two additional dessert options to the menu, determine how many more meal combinations become available. (1 mark) c) On a particular evening, the restaurant runs out of the Soup and Salad entrées. Determine the number of valid three-course meal combinations that can still be ordered that evening. (1 mark)
A security system requires a four-character access code. The first character must be a letter from the set {A, B, C, D, E, F}, the second and third characters must be digits from 1 to 9 inclusive, and the fourth character must be a symbol from the set {#, @, *, %}. (a) Use the multiplication principle to determine the total number of different access codes that can be formed. (1 mark) (b) Determine the number of access codes in which the two digits are identical. (1 mark) (c) Hence determine the number of access codes in which the two digits are different. (1 mark)