Advertisements
Advertisements
Question
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Advertisements
Solution
When tossing a coin, the possible outcomes are head
and tail.
Total number of outcomes of heads and tails on tossing a coin 8 times is
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 28
The number of ways of getting six heads and 2 tails
= `(8!)/(6! xx 2!)`
= `(8 xx 7 xx 6!)/(6 xx 2 xx 1)`
= 4 × 7
= 28 ways
APPEARS IN
RELATED QUESTIONS
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
If nP4 = 12(nP2), find n.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
