Answer : To form a parallelogram we need 2 sets of 2 parallel lines intersecting the other 2 lines from the other set. So, first of all, we need to get 2 lines from the sets. From the first parallel...
Answer : Each committee consists of 3 men and 2 women. So, we need to select 3 men out of 6 and 2 women out of 4. The number of ways, 3 men can be selected out of 6, is = 6C3 = 20 The number of...
Answer : There are 4 bowlers in 13 player team. So, maximum we can add 4 bowlers. And we need to include at least 3 bowlers. If we include 3 bowlers then from the remaining 9 [13 – 4 bowlers]...
Answer : We need to include at least 2 women. If we include 2 women in the committee, then a number of men is 3. The number of ways, 2 women can be selected out of 4 is = 4C2 = 6 The number of ways,...
Answer : To get a straight line we just need to join two points. There are 12 numbers of points. Therefore, there is 12C2 = 66 number of straight lines. Among the 12 points, there are 3 points which...
Answer : Three persons enter a compartment where 5 seats are vacant. The number of ways they can be seated is = 5P3 = 60.
Answer : n-sided polygon has n numbers of vertices. Diagonals are formed by joining the opposite vertices from one vertex, except the two adjacent vertices. So, from one vertex (n-3) diagonals can...
Answer : 3 consonants out of 5 consonants can be chosen in 5C3 ways. 2 vowels out of 4 vowels can be chosen in 4C2 ways. And also 5 letters can be written in 5! Ways. Therefore, the number of words...
Answer : Given: (n2–n)C2 = (n2–n)C4 = 120 Need to find: Value of n (n2–n)C2 = (n2–n)C4 = 120 We know, one of the property of combination is: If nCr = nCt, then, (i) r = t OR (ii) r + t = n Applying...
Answer : ⇒ 5C1 + 5C2 + 5C3 + 5C4 + 5C5 ⇒ 6C2 + 6C4 + 1 [As 5C5 = 1] ⇒ 15 + 15 + 1 ⇒31
Answer : Given: 35Cn+7 = 35C4n–2 Need to find: Value of n We know, one of the property of combination is: If nCr = nCt, then, (i) r = t OR (ii) r + t = n Applying property (i) we get, ⇒ n + 7 = 4n –...
Answer : Given: nCr+1 = nC8 Need to find: Value of 22Cn We know, one of the property of combination is: If nCr = nCt, then, (i) r = t OR (ii) r + t = n We are going to use property (i) nCr+1 = nC8...
Answer : Given: 20Cr+1 = 20Cr–10 Need to find: Value of 10Cr We know, one of the property of combination is: If nCr = nCt, then, (i) r = t OR (ii) r + t = n We can’t apply the property (i) here. So...
Answer : Given: 20Cr = 20Cr–10 Need to find: Value of 17Cr We know, one of the property of combination is: If nCr = nCt, then, (i) r = t OR (ii) r + t = n We can’t apply the property So we are going...