In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. Find the number of ways in which this can be done.
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In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions from the 8 questions in section B. Find the number of ways in which this can be done.
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The digits of the number 6 378 129 are to be arranged so that the resulting 7-digit number is even.
Find the number of ways in which this can be done.
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[2]
[2]
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A team of 3 people is to be selected from 4 men and 5 women. Find the number of different teams that could be selected which include at least 2 women.
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A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if
[1]
[2]
[1]
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Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.
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A 4-digit code is to be formed using 4 different numbers selected from 1, 2, 3, 4, 5, 6, 7, 8 and 9. Find how many different codes can be formed if
there are no restrictions,
only prime numbers are used,
two even numbers are followed by two odd numbers,
the code forms an even number,
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[1]
[1]
[4]
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[1]
[3]
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4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if
[1]
[1]
[3]
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A photographer takes 12 different photographs. There are 3 photographs of sunsets, 4 of oceans and 5 of mountains.
The photographs are arranged in a line on a wall.
Three of the photographs are selected for a competition.
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Given that , find the value of .
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The number of combinations of items taken 3 at a time is . Find the value of the constant .
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The number of combinations of items taken 3 at a time is 6 times the number of combinations of items taken 2 at a time. Find the value of the constant .
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