(Q). In an examination a student has to write 8 papers & has to pass in each paper to pass the exam. In how many ways a student can fail in the exam?Solution:- For every paper there are 2 ways of selection → Pass or Fail.So total number of ways is 2⁸ = 256 &...
(Q). In class (V) there are three sections A, B & C with number of students 50, 70 and 90 respectively while in class (vi) there are three sections A, B & C with number of students 70, 90 & 50 respectively. In how many ways 15 students can be selected...
(Q). In how many ways 8 distinct alphabets can be selected so that no vowel is selected?Solution:- total alphabets = 26 vowels = 5 consonants = 26 – 5 = 21 so we have to select 8 consonants out of 21 consonants & this can be done...
(Q). Given 6 different green dyes, 5 different blue dyes & 4 different red dyes, the number of combination of dyes which can be chosen taking at least one green & one blue dye is?Solution:- one or more (at least one) green dye can be chosen in ⁶C₁ + ⁶C₂ + ⁶C₃...
(Q). How many different sums can be formed with the following coins:⟶ one 1 ruupee, one 50 paise, one 25 paise, one 10 paise & one 5 paise coins? Solution:- Method (1).Every coin has 2 ways of selection:⟶ either selected or not...
(Q). At an election three wards of a town are canvassed by 6, 7 & 10 men repectively. If there are 30 volunteers, in how many ways can they be allotted to different wards?Solution:- 1st we will select 6 out of 30 in ³⁰C₆ ways then next 7 out of 24 in ²⁴C₇ ways...
(Q). In how many ways 5 vowels & 6 consonants can be selected from 26 letters of alphabet?Solution:- vowels = a, e, i, o, u ⟹ total 5∴ 5 vowels can be selected only 1 way& 6 consonants can be selected from 21 consonants in ²¹C₆ waysHence total number of ways =...
(Q). Find the number of ways of selecting 11 players from a group of 35 iplayers such that the oldest & the youngest players are always included in the group.Solution:- Since the oldest & the youngest players i.e. 2 particular players are always included in...
(Q). In how many ways 5 players can be selected out of 10 players(i). If Ankit & Rahul are always selected(ii). If Ankit & Rahul are always rejected.Solution:- (i). ⁸C₃ ways(ii). ⁸C₅ ways ...
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