Permutation & Combination Questions

Solution : If out of n points,  m are collinear, then Number of triangles = $^nC_3$ – $^mC_3$ $\therefore$  Number of triangles = $^{10}C_3$ – $^6C_3$ = 120 – 20 = 100 Similar Questions How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which no two S are […]

Solution : Given, $T_n$ = $^nC_3$ $T_{n+1}$ = $^{n+1}C_3$ $\therefore$ $T_{n+1}$ – $T_n$ = $^{n+1}C_3$  – $^{n}C_3$  = 10  [given] $\therefore$ $^nC_2$ + $^nC_3$ – $^nC_3$ = 10 $\implies$ $^nC_2$ = 10 $\therefore$ n = 5 Similar Questions How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which

Solution : n(S) = $^{10}C_4$ = 210 n(E)= $^5C_2 \times ^3C_1 \times ^2C_1$ + $^5C_1 \times ^3C_2 \times ^2C_1$ + $^5C_1 \times ^3C_1 \times ^2C_2$ = 105 $\therefore$ P(E) = $105\over 210$ = $1\over 2$ Similar Questions How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which no

Solution : 5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 : Total number of ways : ($5!\over 3!1!1!2!$ + $5!\over 2!2!2!$) $\times$ 3! Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = $3^7$ (as

Solution : There are 4 odd digits (1, 1, 3, 3) and 4 odd places(first, third, fifth and seventh). At these places the odd digits can be arranged in $4!\over 2!2!$ = 6 Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in $3!\over 2!$ = 3 ways Therefore, 

Solution : First of all, arrange all letters of given word alphabetically : ‘ADIPR’ Total number of words starting with A _ _ _ _ = 4! = 24 Total number of words starting with D _ _ _ _ = 4! = 24 Total number of words starting with I _ _ _ _