Math Assignment Help With Practical Problems
11.3 Practical problems:
Example 1: In how many ways can a cricket team be chosen out of a batch of 20 players, if
i) there is no restriction in the selection;
ii) a particular player is always been chosen;
iii) a particular player is never chosen;
solution: i) the number of ways In which 11 players can be chosen out of 20 players;
here, n= 20 and r = 11
C(20,11) = C(20, 20 – 11) = C(20, 9)
= 20!/ 9! (20 – 9) !
= 20x19x18x17x16x15x14x13x12/ 9x8x7x6x5x4x3x2x1
ii) when a particular player is chosen always;
= C(19, 10) = C(19, 9)
= 19 x 18x17x16x15x14x13x12x11/ 9x8x7x6x5x4x3x2
i) when a particular player is never chosen;
= C(19, 11) = (19, 2)
= 19 x 18/ 2
Example 2: In an examination, a candidate has to pass in each of the 5 subjects. In how many ways can he fail.
Solution: the student can fail by failing in 1 or 2 or 3 or 4 or 5 subjects out of 5 in each case.
Therefore, the total number of ways in which he can fail
= C(5, 1) + C(5 2) + C(5, 3) + C(5, 4) + C(5, 5)
= C(5, 1) + C(5 2) + C(5, 2) + C(5 1)
[using C(n, r) = C( n, n- r)]
Example 3: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Solution: the number of ways of selecting
therefore the number of group each containing 3 consonants and 2 vowels = 210
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