{"id":1907,"date":"2025-01-15T08:45:15","date_gmt":"2025-01-15T08:45:15","guid":{"rendered":"https:\/\/donhit.com\/en\/?p=1907"},"modified":"2025-02-07T09:12:59","modified_gmt":"2025-02-07T09:12:59","slug":"binomial-coefficient","status":"publish","type":"post","link":"https:\/\/donhit.com\/en\/calculator\/binomial-coefficient\/","title":{"rendered":"Binomial Coefficient Calculator"},"content":{"rendered":"<p><center><div class=\"calculator\">\r\n        <h2>Binomial Coefficient Calculator Tool<\/h2>\r\n        \r\n        <div class=\"input-group\">\r\n            <label for=\"n\">n (total items)<\/label>\r\n            <div class=\"input-wrapper\">\r\n                <input type=\"number\" id=\"n\" placeholder=\"Enter n\" min=\"0\">\r\n            <\/div>\r\n            <div class=\"error\" id=\"n-error\">Please enter a valid number (n \u2265 0)<\/div>\r\n        <\/div>\r\n\r\n        <div class=\"input-group\">\r\n            <label for=\"k\">k (items to choose)<\/label>\r\n            <div class=\"input-wrapper\">\r\n                <input type=\"number\" id=\"k\" placeholder=\"Enter k\" min=\"0\">\r\n            <\/div>\r\n            <div class=\"error\" id=\"k-error\">Please enter a valid number (0 \u2264 k \u2264 n)<\/div>\r\n        <\/div>\r\n\r\n        <button onclick=\"calculate()\">Calculate<\/button>\r\n\r\n        <div class=\"result\" id=\"result\">\r\n            <h3>Result:<\/h3>\r\n            <p id=\"result-value\"><\/p>\r\n        <\/div>\r\n\r\n        <div class=\"formula\">\r\n            Formula: C(n,k) = n! \/ (k! \u00d7 (n-k)!)\r\n        <\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n        function factorial(num) {\r\n            if (num === 0 || num === 1) return 1n;\r\n            let result = 1n;\r\n            for (let i = 2n; i <= BigInt(num); i++) {\r\n                result *= i;\r\n            }\r\n            return result;\r\n        }\r\n\r\n        function binomialCoefficient(n, k) {\r\n            if (k > n) return 0n;\r\n            if (k === 0 || k === n) return 1n;\r\n            \r\n            \/\/ Optimize calculation by using smaller k\r\n            k = Math.min(k, n - k);\r\n            \r\n            let numerator = 1n;\r\n            let denominator = 1n;\r\n            \r\n            for (let i = 0; i < k; i++) {\r\n                numerator *= BigInt(n - i);\r\n                denominator *= BigInt(i + 1);\r\n            }\r\n            \r\n            return numerator \/ denominator;\r\n        }\r\n\r\n        function showError(elementId, show) {\r\n            const element = document.getElementById(elementId);\r\n            element.style.display = show ? 'block' : 'none';\r\n        }\r\n\r\n        function calculate() {\r\n            const nInput = document.getElementById('n');\r\n            const kInput = document.getElementById('k');\r\n            const resultDiv = document.getElementById('result');\r\n            const resultValue = document.getElementById('result-value');\r\n\r\n            const n = parseInt(nInput.value);\r\n            const k = parseInt(kInput.value);\r\n\r\n            \/\/ Reset errors\r\n            showError('n-error', false);\r\n            showError('k-error', false);\r\n\r\n            \/\/ Validate inputs\r\n            let hasError = false;\r\n\r\n            if (isNaN(n) || n < 0) {\r\n                showError('n-error', true);\r\n                hasError = true;\r\n            }\r\n\r\n            if (isNaN(k) || k < 0 || k > n) {\r\n                showError('k-error', true);\r\n                hasError = true;\r\n            }\r\n\r\n            if (hasError) {\r\n                resultDiv.classList.remove('show');\r\n                return;\r\n            }\r\n\r\n            \/\/ Calculate result\r\n            const result = binomialCoefficient(n, k);\r\n            \r\n            \/\/ Display result\r\n            resultValue.textContent = result.toString();\r\n            resultDiv.classList.add('show');\r\n        }\r\n\r\n        \/\/ Add event listeners for input validation\r\n        document.getElementById('n').addEventListener('input', function() {\r\n            showError('n-error', false);\r\n        });\r\n\r\n        document.getElementById('k').addEventListener('input', function() {\r\n            showError('k-error', false);\r\n        });\r\n    <\/script>\r\n<\/center>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[184],"tags":[],"class_list":["post-1907","post","type-post","status-publish","format-standard","hentry","category-calculator"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - 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