Permutations Combinations 1-6

31 For an examination, a candidate has to select 7 subjects from three different groups X, Y and Z which contain 5, 6 and 4 subjects respectively. In how many different ways can a candidate make his selection if he has to select at least 2 subjects from each group?

A2400
B2700
C3000
D3200


32 A box contains 3 different White balls, 4 different Blue balls, 5 similar Green balls. In how many ways can 3 balls be drawn the box so that at least 1 blue ball is always included in the draw?

A50
B52
C56
D60


33 Out of 3 mathematics books, 4 science books, and 5 literature books (all are different), how many different collections can be made by taking $atleast$ one of each kind?

A$7 \times 16 \times 32$
B$8 \times 15 \times 31$
C60
D$3! \times 4! \times 5!$


34 What is the number ways of selecting 4 articles out of 10 articles? Given that 3 out of these 10 articles are identical.

A98
B90
C120
D24


35 In how many ways can a pack of cards be equally divided among two players?

A$\dfrac{{52!}}{{26! \times 26!}} \times 2!$
B$\dfrac{{52!}}{{26! \times 26!}}$
C$\dfrac{{52!}}{{26! \times 26!}} \times \dfrac{1}{{2!}}$
D$\dfrac{{52!}}{{26!}} \times 2!$


36 In how many ways can 10 identical items be distributed among 6 students so that each student gets at least one item?

A219
B256
C126
D${}^{15}{C_5}$


37 In how many ways can 10 identical items be distributed among 6 students so that each student gets any number of items?

A$^{{15}} {{C}}_{{4}} $
B$^{{10}} {{C}}_{{5}} $
C$^{{15}} {{C}}_{{5}} $
D$^{{10}} {{C}}_{{4}} $





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