In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
| Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) =$ \left(\dfrac{7 \times 6}{2 \times 1} \times 3\right) $= 63. |
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In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions? |
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Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? |
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In how many different ways can the letters of the word LEADING be arranged in such a way that the vowels always come together? |
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In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate? |
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How many words can be formed by using all letters of the word BIHAR? |
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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? |
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In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together? |
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In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? |
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There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? |
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In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? |
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